We have primary documents supporting a very small subset of what he says. Most of the claims, including the more extraordinary ones such as he can wiretap anyone in the world including Barack Obama's personal email from his desk, remain undocumented.
You're missing the point: Nobody's denying that with the right internal authorization, the NSA can tap any phone line they like. What's up for debate (since Snowden has provided no evidence) is the claim that Snowden could do it all by his lonesome, with no oversight or approval.
While I disagree with your point as well, I don't think it's at all the point to which I was responding. The question was about the credibility of his claims. I have not heard any other NSA whistleblower doubting his claims, and in fact they all seem to corroborate them.
Snowden directly addresses your point in his live chat:
"More detail on how direct NSA's accesses are is coming, but in general, the reality is this: if an NSA, FBI, CIA, DIA, etc analyst has access to query raw SIGINT databases, they can enter and get results for anything they want. Phone number, email, user id, cell phone handset id (IMEI), and so on - it's all the same. The restrictions against this are policy based, not technically based, and can change at any time. Additionally, audits are cursory, incomplete, and easily fooled by fake justifications. For at least GCHQ, the number of audited queries is only 5% of those performed."
http://www.guardian.co.uk/world/2013/jun/17/edward-snowden-n...