That's not the way logic works. Affirmative assertions need to be demonstrated by the person making the claim. It's not encumbent on anyone to disprove Snowden's claims; it's his responsibility to show that they are true.
The weird thing is the NSA has never refuted the very specific allegation of Booz's access and the lack of supervision (http://www.theguardian.com/world/2013/jun/09/edward-snowden-...), merely just repeated that 'oversight exists'. Since we're all discussing a massive series of leaked documents, how do you logically think otherwise?
Let's see what the Office of the Inspector General (OIG) has to say: