A leak is, if verified, is both allegation and proof. The leak would be an actual NSA document, which the NSA didn't want made public. If they did, its wouldnt be a leak, it would be public record. If the leak was not true, it would not be a leak, it would be a lie, a fiction. The NSA don't even claim that. So, yes, we believe the leak.
A statement by the NSA is simply what they want to say. It cant be proven or verified, you have to take their word for it. Now, if the NSA were to release verifiable documented proof, then we would have to consider that. But it still is not as powerful as a real leak. It can't be because a NSA release has potential for manipulation since they are the source of the release.
Yes, real leaks from a given source are much more believable than statements from that source. Which is why, time to time, governments like to release information in the form of a leak. So, we do have to be very careful about where leaks come from. In the case of Snowden's leaks, I believe we can be sure that they are real and not a very clever manipulation by the NSA or US government.
So, yes, a lot of people would believe the "leak says" over "the NSA says". Rightly too.