It's a fascinating discovery, and I too say hats off to Black Rabbit, Further Glory and Carolyn.
That said, and while I agree that the Standing Man image shows clear signs of cut-and-paste fakery, I think that we shouldn't dismiss the possibility that the original NYT image was tampered with as well.
The problem is the contrast between the background darkness and the woodwork of the bunks on one side, and the square pillar on the other. If you look at the high-res (Standing Man) image, the contrast is clear on both sides, with the bunks and pillar standing out about equally well. In the NYT image, however, while the woodwork of the bunks is in high (even overexposed) contrast with the background darkness, the pillar on the right is so dark itself that it all but disappears:
no contrast.

Even if we allow for a slight difference of contrast levels between bunk/background and pillar/background in the high-res image, it's pretty clear that that difference wouldn't be enough to account for the difference in the NYT image. In other words, if the contrast is sharp on the bunk side in the NYT picture, it should be about as sharp on the pillar side as well. Instead, we have the bright woodwork against a black background on the bunk side, and the pillar disappearing into the darkness on the other. Since the pillar clearly was there in the barrack (I think we can trust the high-res image to tell us that much) and exposed to the same light source, the natural conclusion is that in the NYT version it has been deliberately obscured.
In other words, you could just as easily make the case that something (the Standing Man?) was removed from the NYT image, and that the photo manipulator then darkened that side of the print in some way to hide the traces of tampering. After all, if someone had been standing in front of the pillar and you cut his image out, it would be much easier to cover up the hole which that would leave in the picture if you put the pillar in deep darkness.
As for why the paper might have resorted to such a trick, one can only speculate, but assuming (for the sake of argument) that it was indeed the Standing Man that got rubbed out, it seems reasonable that an editor might have worried about how readers would react to seeing a naked "Mussulman" staring out at them from page 2. Later, when other actors in the disinformation/media complex realized the potential propaganda value of such a "shocking" image, that one-time decision could then have been reversed, such that the unretouched (or re-retouched?) image was put back into circulation as we have it today.
Of course it could be objected that excising the figure by the pillar and then darkening the print on that side is a lot of bother when the photo editor could simply have cropped the image. But if you try it, you get a rather truncated image: it looks obviously cut off.

So rather than spoil the "frame" of the picture, the decision could well have been made to simply eliminate the offending element(s) from it, and then cover up the traces with black.
As I said above, I actually agree that the Standing Man image looks faked. The blurry edging along his left arm seems clear evidence of tampering, and his toes are in line with or even behind the front side of the pillar while his arm and shoulder are in front of it. (Kind of an awkward way to stand, don't you think?) So yes, there's something fishy with that picture too, no doubt about it. I just raise the question of tampering in the NYT version because I know that if I wanted to defend the exterminationist interpetation that's the tack I'd take: I'd say that Standing Man really was there all along, and was blacked out by the NYT out of respect for the sensibilities of its readers. And frankly, I think the evidence for some kind of tampering is indeed there: the difference in contrasts tells the tale.
So how to respond to that argument?