I would've guessed the same thing, but it looks like he hasn't been dead for long. I'm almost alarmed that we got the announcement without DNA testing having been completed (as appears to be the case), and no photos or videos have been forthcoming as of yet. This can only fuel conspiracy-minded chatter, even if temporarily.
Assuming this is even true, it was faked before the news came out and was thus an inside job. What possible reason would they have for doing this? How do these tweets improve the position of the US?