Marc Ambinder, a reporter who has covered the national security beat for many years (before that he was a political reporter for The Atlantic, and before that the White House reporter for --- I think? --- CBS), reported that PRISM is a system of dropbox servers and a user interface that allows seamless access to all of those servers, presumably so that analysts don't have to keep track of which data is affiliated with Google and which data is affiliated with Yahoo.
Other reports have corroborated this.
Declan McCullagh, who has covered this beat for CNet for something like 10 years and is most notable on HN for jumping into threads and arguing the EFF's side of any given story against me (in other words: not a guy prone to support of the establishment), ran a story last week with sources that also denied that NSA had unilateral access to Google Mail.
The NYT just a few days ago ran a story with a linked FISA court order that documented Yahoo's attempt to push back on a FISA directive, a process that would not have been necessary (for the government) had NSA had direct access to Yahoo's servers; the court order demanded that Yahoo turn over data.
And, of course, Google categorically denies that NSA has direct unilateral access to their servers and, for that matter, that they've been able to obtain records for large fractions of their user base. Those denials have come from multiple levels of the company, from the CEO to the General Counsel to their tech leaders to people on their security team.
I'm not simply supposing that NSA doesn't have this access. Based on the evidence available, I am drawing the obvious conclusion that they do not.