The people backing him would be really going against the grain since Greenwald is pretty anti-establishment.

Snowden provided material to both Washington Post and the Guardian, but it was the Guardian that chose to really dive into it and milk it all the way -- Washington Post hesitated. A lot of people are hungry for Greenwald giving them more Snowden leaks, the backer probably understands this.

The understanding with Greenwald is he's not afraid to piss off people -- if he gets more leaks in his hands, he's going to let the public in on it. It's hard to imagine Bezos getting himself into this kind of public hot grounds, so I think it's highly unlikely that Bezos is behind this.

edit: small grammar fix; thanks cpeterso