Probably the best written and the earliest popular exposition of the
evolution of the body fluids in the vertebrate animals is "From Fish
to Philosopher" (John Wilkins, take note -- you have lots of finny
competition!) by Homer Smith.  I believe it was originally published
in 1953 by Little, Brown.   My copy is a special paper edition put out
by Ciba Pharmaceuticals in 1959.  The subtitle is "The Story of Our
Internal Environment" and it describes exactly the problem you raise
as well as the evolution of the vertebrate and the mammalian kidney.
Dr. Smith was a noted renal physiologist who spent some 30+ years
studying that particular subject. For more current discussions, see
"Animal Physiology: Adaptation and Environment" by K. Schmidt-Nielsen,
5th Edition, 1997, Cambridge U Press although I must confess that I
only have the 4th edition,  1990.  The subject has not been modified
drastically in the last 15 years.  Another excellent source is "Eckert
Animal Physiology: Mechanisms and Adaptations", by Randall, Burggren,
and French, 5th Edition, 2002, Freeman.  That one I do have and have
taught from for many years going back several editions. These two are
probably the most widely used textbooks in Animal Physiology. Many
good introductory biology textbooks, the encyclopedic ones
specifically written for biology majors, also treat the subject.

In order to explain the situation to you, I am afraid I have to go
into quite a bit of background to prepare you for the argument.
Fortunately for me, I am a college professor and lecturing at you
comes quite naturally. Unfortunately for you, if you want to
understand what I am saying, you will have to read all this.  Normally
it would take at least a full hour lecture with explanations and
examples and so on. You would also get my atrocious jokes.  I will try
to be as brief as I can, but still try to be at least a bit
understandable and to leave out my attempts at humor.

The most important basic fact of physiology to understand is that
osmotic regulation is a really major problem for animals.  Animal
cells have no cell wall and cannot withstand an osmotic difference
between the intracellular and extracellular fluid.  The intracellular
fluid must necessarily be rather concentrated to maintain its
biochemical and biophysical activity.  Hence the extracellular fluid
must be exactly equally concentrated.  The specific salts inside the
cell are quite different from those outside, but the osmotic pressure
is the same so that the cells are in osmotic balance. The  importance
of the "regulation of the internal environment" , which refers to a
major degree to just this osmotic regulation, was proposed by C.
Bernard in the mid 19th Century and is considered one of the major
landmarks in the beginning of the subject of physiology.

The interface between the inside of the cell and the outside across
the cell membrane is only part of the problem.  The other part is the
interface between the extracellular fluids outside the cell, but
inside the organism, (that is, the body fluids) and the external
fluids; fresh or salt water (terrestrial animals are a special case
and are treated separately). There is no special reason why the body
fluids (including the blood plasma) should be the same osmotic
concentration as the external environment except for the very  big
fact that it is an enormous metabolic expense to regulate the body
fluids if they are different.  Even if you make the external surface
relatively impermeable, the gills are necessarily directly exposed to
the external environment, they have very large surface area and are
extremely permeable to oxygen and carbon dioxide. One of the examples
of "incredibly poor design" in animals is our inability to produce a
membrane permeable to gases but not to salts and to water.  As a
result, any difference between the body fluids and the environment
means a very large osmotic exchange of water and a diffusion exchange
of salts that must be compensated somehow.

There are basically three ways of living in water.  If your body
fluids match the environment, you have no problem -- life is easy.
This is the way virtually all marine invertebrates live.  They do have
body fluids virtually the same as sea water.  They may have somewhat
different Ca++ and Mg++ concentrations than sea water, but that the
NaCl concentration is pretty close as is the osmotic pressure.  Hence
they have an easy life. You might expect all marine creatures to live
this way, but no -- see below.

The second way is to have body fluids significantly more concentrated
than the environment.  That is the situation for all fresh-water
animals.  Fresh water is so dilute there is no way to allow the body
fluids to match it because that would require the intracellular fluids
also to match it which appears to be incompatible with life.  So to
keep the cells happy, the body fluids must be salty, hence must be
more concentrated than the environment.  Therefore these animals are
constantly taking in water by osmosis and losing salt.  As a result,
these animals never drink and seek a source of salt in their food.
They also have evolved excretory organs (kidneys, in the case of the
vertebrates) specialized in producing a very large volume of urine
with special mechanisms to reabsorb as much salt as possible from the
urine.  They also have special mechanisms in their gills and their gut
to actively transport salts from the very dilute water they live in to
the more concentrated body fluids.  These pumps use a substantial
fraction of their metabolic energy, a severe evolutionary load.
However they have no choice and, besides, all their competitors in
fresh water have exactly same problem.  Fresh water fish and
amphibians live this way, as do fresh water worms, annelids,
crustacea, and insects. Note in particular two things.  First, these
vertebrates have kidneys  specialized to produce large volumes of very
dilute urine and INwardly directly active transport systems (towards
the body fluids) in kidney and other organs. (Invertebrates are
similar, but their excretory organs are not kidneys and work a bit
differently). Second, these vertebrates have body fluids significantly
less concentrated than sea water, in fact roughly  1/3 the
concentration of sea water.  That fact means the problem is not as
severe as it might be if their body fluids were, indeed, as
concentrated as sea water.

The third way to live is to have body fluids significantly more dilute
than the environment.  This is the situation for virtually all
salt-water fish, as well as reptiles, birds, and mammals that live
oceanic lives and never encounter fresh-water.  Because of this
imbalance, they constantly lose water to the environment by osmosis
and take on salts by diffusion.  To compensate, they must constantly
drink (only salt water fish actually "drink like a fish", fresh-water
fish never drink!) and must excrete a very tiny volume of extremely
concentrated urine.  Also they must have OUTward directed active
transport systems to eliminate the salt.  Not only is it a surprise to
find out that these animals do exist -- their lives would be much
simpler if they just had body fluids the same as sea water.  But it
turns out that their kidneys are totally unable to produce
concentrated urine or to transport salts in the OUTward direction at
all!  They have extremely reduced kidneys that produce tiny volumes of
urine, but that urine is the same concentration as their body fluids.
They do have specialized outwardly directly salt transport systems in
their gills and gut,  So the existence of these animals seems to be a
problem.

Then there is the problem of terrestrial animals.  For simplicity, I
will only consider the terrestrial vertebrates -- amphibians,
reptiles, birds, and mammals (OK, I know there is no such thing as
"reptile", but no matter, the argument still holds). All these animals
have body fluids roughly the same osmotic concentration as fresh-water
fish, roughly 1/3 the concentration of sea water.  In other words,
this completely explains the original question -- why humans have body
fluids significantly less salty than sea water even though life first
evolved in sea water.  The answer is most definitely NOT that oceans
were 1/3 as salty back then.  It most definitely IS that the earliest
vertebrates did evolve in salt water and then moved into fresh water.
As an adaptation to avoid the osmotic effect of living the "type-two"
way described above, they dropped the salinity of their body fluids
about as low as they could consistent with keeping their cells happy.
From then on, all vertebrate evolution (including the lungfish and
lobe-fin fish, the amphibians, the reptiles, the birds, and the
mammals) all retained the ancestral body fluid concentration roughly
1/3 sea water.  (Again, a technical detail.  I am grossly
oversimplifying vertebrate and tetrapod evolution and using incorrect
terms for modern animals to describe the ancient and extinct
transition forms. But that is simply the gross oversimplification
ordinarily used in introductory expositions.  If you wish, replace
"lungfish, lobe-fin fish, amphibian, reptile" with the proper
cladistic term, throw in the dinosaurs (although we don't know what
their body fluids were like) and do it up right.  You still get the
same result.)

Okay, the original question is now answered. However, the full story
is so beautiful and illustrates so well just how evolution is totally
married to physiology, that I must continue.

Terrestrial vertebrates, the tetrapods (amphibians, reptiles, birds,
and mammals) with good access to fresh water don't have the same
problems as fish because (except for larval amphibians) these animals
don't breath with gills.  If you make the skin impermeable, which all
except the amphibians have done, you really don't have the water and
salt exchange problem. However, all these animals still retain the
same physiological pattern as fresh-water fish: a tendency to seek
sources of salt in our food and kidneys specialized to produce large
volumes of very dilute urine using salt transport mechanisms to
reabsorb salt INTO the body from the urine.  Since we don't constantly
take in water osmotically through our gills, we do have a change in
that we constantly seek to drink water.  Except for drinking water, we
have kidneys and physiology "designed" for living in fresh water.

Now what about tetrapods that live either in deserts or in sea water
and do not have access to fresh water?  They constantly lose water by
evaporation and take in salt with their food.  As a result, they share
the same problem with salt-water fish: how to obtain enough water and
how to get rid of excess salt.  Unfortunately, these animals are stuck
with fresh-water kidneys  -- kidneys that produce dilute urine and
salt transport systems that are INward directed.  This is a REALLY BIG
example of INCREDIBLY STUPID design in animals.  Amphibians can't cope
-- they don't live in marine environments.  (Yes, Rana cancrivora
lives in salty mangrove swamps.  It is a special case, see below.
There are always special cases!)  Reptiles and almost all birds, but
especially including the truly marine birds like penguins,
albatrosses, gulls, auks and puffins, ducks, etc cannot produce
concentrated urine at all.  They have evolved specialized glands in
the eyes, nose, and mouth that excrete salt. (Of course these are not
totally new inventions, they are derived from other glands like
lachrymal and salivary glands).  Songbirds (Passeriformes) and mammals
have taken a different tack.  They have devised an extremely clever
trick in kidney structure to allow salt transport pumps which really
take salt back INTO the body from the urine but still manage to use
them to produce urine much more concentrated that their body fluids
and so excrete salt FROM the body. I can't go into that at all here --
it is a counter-current concentrating mechanism which, for mammals,
involves the Loops of Henle in the kidney.  Birds and mammals use a
similar type of  trick but in very different ways, indicating separate
evolution in these two groups.

The story is made even more tantalizing by some other special
exceptions in the vertebrates.  The hagfish has body fluids the same
as sea water, just like invertebrates.  The lamprey has body fluids
more like fresh-water fish.  The explanation is that the earliest
craniates evolved in sea water but virtually all the rest of
vertebrate evolution past the hagfish stage occurred in fresh.  This
was proposed very early in the 20th century from the physiological
data.  I believe this was even before other paleontological evidence
demonstrated that it was correct.  (Although I am sure the vertebrate
paleontologists in this group -- if they got to read this far -- will
promptly correct me).  And, more interesting, it demonstrated that
hagfish and lampreys were not all that closely related even though
they were lumped together as "cyclostomes" until relatively recently.
In other words, the body fluids of hagfish and lampreys very
beautifully illustrate vertebrate evolution. Then most of the rest of
the vertebrates, having evolved in fresh water, developed body fluids
much more dilute than sea water. That is, human blood plasma salinity
is another beautiful illustration of evolution, exactly contrary to
Uncle Davey's claim that it cannot be explained! But wait, it gets
even better!  The sharks are virtually all salt-water fish, but they
have body fluids whose concentration is even slightly  MORE
concentrated than sea water!  How could that be if vertebrates after
lampreys evolved in fresh water?  It turns out that the SALT
concentration of their body fluids is quite consistent with that of
fresh water fish, much more DILUTE than salt water.  But they make up
the difference by all lowing urea to accumulate in their body fluids
to make up the osmotic difference.  As a result they have the same
WATER problem as fresh-water animals (body fluids more concentrated
than their environment) so their kidneys work OK.  However they do
have a SALT problem just the opposite.  Their kidneys can't do the job
-- remember, they inherited a fresh-water kidney. So they evolved
special rectal glands to excrete salt.  Even more interesting, the
Coelecanth, that "fossil relic" of a lobe-fin fish discovered in deep
oceanic water, does the same trick with urea.  So does that weird
frog, Rana cancrivora, the only amphibian that can tolerate
concentrated salt.  These illustrate convergent evolution -- a similar
mechanism evolving quite independently in different groups to solve
the same problem.  Of course, there is no "irreducible complexity"
involved -- vertebrate kidneys are very good at producing urea and
vertebrate kidneys are ordinarily very good at excreting it.  It
doesn't take that much change to retain the urea and urea is not all
that toxic or dangerous so having the cells develop a tolerance to it
is not all that difficult.  The salt-water fish have a better solution
(see below) but they evolved separately from these others.  Evolution
doesn't always pick the best solution, just one that works well enough
to keep you in the game.  Another nice illustration of evolutionary
principles.

So what about salt-water fish? Since they derived from fresh-water
fish that then migrated back out to the ocean, they inherited kidneys
and body fluids totally unsuited for the job.  So many of them simply
let their kidneys shrink into insignificance -- they are not that
useful.  They drink to take in water and have gill and gut OUTward
transport systems to eliminate the salt.  This seems much more
effective than the urea trick.  The only way you can easily understand
this situation is to realize that they did in fact originate in
fresh-water.  Again, the evolutionary pattern exactly matches the
physiology.  Even more -- there are fresh water fish that have
extremely reduced kidneys and have even weirder mechanisms to regulate
body fluids.  It turns out that these guys evolved from sea water fish
that migrated back to fresh water!  In other words, the pattern of
evolution went from seawater (earliest craniates) to fresh (later
craniates and teleosts) to seawater (saltwater teleosts) to fresh
(this weirdos).  

I have already covered the extremely strange situation of desert and
salt water mammals. Even humans live in rather arid climates and often
have little fresh water available.  We can produce concentrated urine
(though not nearly as concentrated as desert and marine mammals) but,
remember, we too inherited kidneys totally unsuited for the task.
Remember, the basic freshwater pattern is to produce lots of dilute
urine but desert dwellers must produce a small amount of concentrated
urine.  So evolution to the rescue once again: build a Loop of Henle
and use the INward directed salt pumps to simulate an OUTward directed
transport system, hence get concentrated urine.  Evolution wins,
again!

Yes, I am getting just a little punchy, but this is a subject I truly
love.  Everything about biology, including human physiology, is a
beautiful product of the evolutionary process.  Read Homer Smith to
get a more temperate and literate discussion of all this.

So, Uncle Davey, your claim that "the sea must have been a lot less
salty than it is now" is completely wrong.  You point that "in
saltwater cells need additional resources to those needed in
freshwater in order to osmoregulate" is entirely wrong for salt water
invertebrates, for hagfish, and for any other animal that evolved in
saltwater and remained their.  It is true for salt water fish because
they evolved from fresh water varieties.  The pattern of blood plasma
salinity in humans and in all vertebrate animals and, indeed, in all
animals is a beautiful exposition of evolutionary principles, not a
contradiction of evolutionary predictions.