The NSA analyst gets intel on such-and-such an account ID/phone number/email/etc., uses PRISM to send a request (probably something stupid like SOAP, it's the govt after all).
The company computer verifies a valid warrant ID, valid request type, "hoovers up" the data requested and spits it back to NSA.
Technically not direct access. Certainly not a direct wiretap into the entire company database. But NSA is able to get the "special source data" they need for correlation on their end (possibly using tools as provided by Palantir).
They figure out whatever network of conspirators they're researching, develop "actionable intel", good guys win (note: depends on your interpretation of good guys, obviously :P).
Zuck and Page are still right in this scenario. I just wish someone would speak up about what the hell is actually going on!