Sure, but the statement as worded does not rule out the possibility that a third party contractor (Palantir) has access, and feeds it to the government. So Google has the motive (some theoretical secret law they need to abide) and they haven't denied a potential means (third party mediation). That's enough for people to convict in this situation.
Sure.
The statement does not rule out the possibility that aliens are using advanced technology to watch the bits on optical lines without affecting the photos either.
True. However, the prior probability of that statement being true is exceedingly remote, so a non-denial of that still leaves me relatively certain that I don't have to worry about aliens conspiring with the federal government to spy on me.
"prior probability" is a fancy way of saying "without evidence, I believe what I want". Not that there's anything wrong with that, but that's not something Larry Page can help you with.
> First, we have not joined any program that would give the U.S. government—or any other government—direct access to our servers.
You would be hard pressed to argue that "direct" access proxied through a gov't contractor isn't the same as direct access. I don't think they'd cut the truth that close unless they were under oath. The court of public opinion is less caring of technicalities.
They say "we do not provide direct access", because as explained, any access goes through proper legal channels.
I'm not sure what you'd call it?
Remember language matters, and these are actionable public communications.