Can we trust this though? “Cooperate with us and we’ll leak fake stories about how frustrated we are with you as cover”.

And I’m not singling out Anthropic. None of these companies or governments (i.e. people) can be trusted at face value.

They don't do that. They're not capable of cooperating with anyone, it's maximum punishment all the time. It's unclear if they can keep secrets either.

Yeah, and a private capitulation doesn't accomplish their goals either. They want the spectacle of public submission.