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.
This is interesting since I'm sure the feds want cooperation from Amazon, and hence Bezos. If Bezos is behind it, then that might make some sense - NSA forces Bezos to comply with whatever they want, and this is his way of fighting back.
However, the first interview by Greenwald was given to the Washington Post -- which Bezos just purchased.