Not the video, of course, but the puppy itself. Ace says yes; I say maybe. Compare and contrast the screencaps to the magically realistic fake sleeping dog. Do we have our pup?

The one in the video seems not quite so … plush, but exposure to the elements in Iraq would do that to a toy, I guess. And the similarity of the markings is quite a coincidence.

Update: And maybe nothing more than a coincidence. Commenter “Limerick” says he has one of those fake dogs at home and the underside of it is completely flat. You can’t change its posture.