The CEO is an instrument of the board. The CEO is not there to lead the board. This is just backstabbing, plain and simple.
Not that that's actually ever going to be the case at OpenAI again, but the parent has the chain of command here totally bass-ackwards.
In theory, yes. In practice: Not always.
In truth it's both. That said, leadership doesn't mean lying. Particularly not about what another person has said. Very particularly not when it's trivial for them to compare notes.