I think that some of those people have knowledge of a secret program that enables access to the data (maybe without direct access to the servers that house it). That would make it easier to manage without having to bring all the SREs and such into the conspiracy.
I think that most of those people would not allow their lives to be destroyed with federal charges (or maybe even extralegal harassment, who knows - they do run secret prisons) in the process of reporting such a thing.
Tens of thousands of others have chosen to keep quiet about NSA's extralegal collection practices (from the contractors at the IXes installing beam splitters, to the mechanics who welded the fiber grabber arm onto the nuclear sub). Why is it such a stretch to think that 3 or 5 or 10 at Google wouldn't?
It's not even a stretch to think that NSA would have done their homework to know _which_ people inside of Google would be both able to participate and could be coerced into keeping quiet.
People that think the "manual" part in that last sentence doesn't matter should read the court order in the Yahoo case the NYT reported, where Yahoo went several rounds with NSA and the FISC to try to fight a specific FISA directive.
Note that Google, Facebook, and Yahoo have all taken pains to point out that they've pushed back on FISA directives. Which is something you can't do if the system isn't manual.
Just because they've pushed back doesn't mean the system isn't automated. It could have been a matter of "implement the automated system now, per the FISA order, and then we can have a go-round in front of the FISA court with your objections after".
This is military intelligence we're talking about here, they take their mission very, very seriously. I wouldn't be surprised if there were multiple, independent, redundant programs for monitoring this data.
† ... we think; the ultimate Constitutionality of this is up in the air.
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.
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.
Your point, though, absolutely stands.
Moreover, having obtained this illicit access, in direct defiance of the corporation that owns and controls those servers, their use of that access is so routinized that it appeared in a "USE BOTH!" Powerpoint deck for NSA analysts?