The only thing I can offer is that you will need to remind this alleged
endo of yours to pick up any basic endo book and s/he will find statements
such as "the normal range for plasma cortisol and urinary free-cortisol
values overlaps the detection limits of most assays; thus, reliable tests
of AI require evaluation of the ability to respond to ACTH stimulus."
I mean, EVERY freakin' endo book I picked up in the medschool library
said this (I admit that I only picked up 4 of them.....they're big and
heavy suckers).  The 24h urine free-cortisol test is designed to catch
adrenal HYPERfunction, *NOT* hyPOfunction.  

In order to have additional credibility, you MUST *not* appear to be
stressed (as you will see in a couple of passages below).....  If you
are outrageously STRESSED, and return a normal cortisol result instead
of a low one, then they will tell you that you do not have AI....

From http://www.csu.cuhk.edu.hk/~cpy/wardmanual/chemman3.htm#13.2:
<quote>
13.2 Adrenocortical Hypofunction (Addison's Disease)

In general, stimulation tests are required to investigate hypofunction
because a failing adrenal gland may be able to produce adequate basal
levels of corticosteroid despite a severe decrease in its reserve.
Isolated serum cortisol levels are uninformative and urine free cortisol
is of no value.
<endquote>

From http://www.merck.com/pubs/mmanual/section2/chapter9/9b.htm
(I would think that the Merck manual would be a respected resource):
<quote [EMPHASIS ADDED]>
Adrenal insufficiency can be diagnosed by demonstrating failure to
increase plasma cortisol levels, or urinary-free cortisol excretion, upon
administration of ACTH. Urinary-free cortisol excretion in the absence of
exogenous ACTH stimulation is unreliable as an index of adrenocortical
functional capacity, since baseline excretion does not adequately separate
the low-normal from the abnormally low value. A single determination of
plasma cortisol or 24-h urinary-free cortisol excretion [IS NOT USEFUL AND
MAY BE MISLEADING IN DIAGNOSING ADRENAL INSUFFICIENCY]. However, if the
patient is severely stressed or in shock, a single depressed plasma cortisol
determination is highly suggestive. An elevated plasma ACTH level in
association with a low plasma cortisol level is diagnostic.
<endquote>

And from
http://www.labcorp.com/datasets/labcorp/html/chapter/mono/sr011300.ht...
These are the folks that produce the test kits used in many labs...
in regard to the 24h free-cortisol, urine, test....
<quote  [EMPHASIS ADDED]>
Use Evaluate adrenal cortical function, [ESPECIALLY HYPERFUNCTION];
evaluate obese or hypertensive subjects with glucose intolerance, plethora,
round face, hirsutism, striae, backache, irregular menses in various
combinations, most of whom do not have Cushing syndrome. Elevation of
urinary free cortisol in a properly collected specimen in the [UNSTRESSED]
patient is sufficient to diagnose Cushing syndrome, and a normal result is
strong evidence against that diagnosis. This is the [TEST OF CHOICE FOR
THE DIAGNOSIS OF CUSHING SYNDROME]. Urinary free cortisol is a more accurate
reflection of cortisol secretion than a single serum specimen.
<endquote>

And now to a new topic:  Did you know that cortisol is made in your very
own body from....(drum roll).....LDL cholesterol?  Me neither until I
flipped thru one of those hefty endo books to find info about insulin
resistance (which is why I really wanted to look at them anyway, but
I figured while I was there I might as well look up AI).  But it begs
the question:  How is your LDL?  As a mostly vegetarian, I imagine it
is low/low-normal.....

I have to end with an AI joke:  (A)rtificial (I)ntelligence is no match for
natural stupidity.