Is it plausible that having gained that access, their use of it is so routine that it has an official name ("PRISM") and a logo and appears in slide decks targeted at NSA analysts and is used a program whose existence is known outside NSA (there are DOD manuals that refer to the same PRISM program)? No. That is not plausible.
We don't know the intended audience of the slides, either, though with a data source as rich as all of Gmail, presumably there'd be tons of analysts capable of accessing it or else it would just be a waste.
I don't see this hypothesis as being anywhere outside the wheelhouse of the NSA. Even outright infiltration (i.e. the hypothesis that not even Page is in the know) is, well, kind of the point of intelligence services, but it's not necessary.
1. Google is lying. 2. Prism (or the backend thereof) is genuinely unknown to most Google employees. Those few employees who do know of it are lying. The others (i.e. legal) are ignorant because they have no need to know, and because it provides plausible deniability. 3. There exist NSA agents capable of passing a Google interview and installing backdoors, perhaps with the collusion of other agents.
Companies the size of Google are, in software terms, Borg cubes of interacting systems. No one comprehends the whole thing, and some degree of secrecy between services is normal. Who would notice if, say, Gmail traffic was being replicated onto NSA-controlled hardware? A small part of a small part of the Gmail team. No one else would likely notice even if it was done in an obvious way.