I'd like to point out that this problem still exists and it's really really limiting the functionality of my App, since a lot of postings can't be played from within the app but only through an embedded browser.
To give another example,
this fairly new post contains an audio file which can only be accessed through the embedded player, even though it seems to lie on tumblr's servers.
I would really appreciate some feedback here, even if it's only a "Can't be done". Thanks!