What about specific unidentified Google employees known to Larry Page, albeit not Google's General Counsel? (In the paraphrased, immortal words of Al Gore: of course it's illegal, that's why it's a covert operation.)

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 follow. Larry Page and Google's General Counsel jointly signed the denial.

Hypothesis: Page was lying; the General Counsel was in the dark for plausible deniability and genuinely believes to this day that PRISM doesn't exist, at least not in a way that involves Google.

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.

This is just innuendo.

You're overcommitted to the hypothesis that Google is completely uninvolved based on their own denials which carry close to zero informational value.

Given that your hypothesis is rather outlandish even by the NSA's own slides (which explicitly mention 702 compliance) and would require more Google employees than Page to know and willingly lie about it, I don't see why it should take priority over a hypothesis that actually meets all the Occam wickets.

Note that I am not taking sides in this argument in this particular reply, but the PRISM referred to in the leaked manuals appears to be an entirely separate program, for managing responses to emergency events.

I understood there to be references to both; to other DOD programs called "PRISM", and to programs called "PRISM" that probably are the NSA program. Other DoD agencies are clients of NSA.