I can think of at least two high status individuals I've met in the corporate world that displayed a wide range of intelligence depending on their audience.
Which audiences elicited which behaviors? From your hypotheses, it sounds like they were smarter in front of higher status people. But Technologos's hypothesis is opposite.
I don't think they acted smarter around higher status people or dumber around low status people.
Smarter around people who were already convinced of their high status and authority, perhaps. And dumber around people whom they knew less well or who knew them less well.
ETA: I never observed them when they were trying to impress their bosses, though.
Michael Vassar once suggested: "Status makes people effectively stupid, as it makes it harder for them to update their public positions without feeling that they are losing face."
To the extent that status does, in fact, make people stupid, this is a rather important phenomenon for a society like ours in which practically all decisions and beliefs pass through the hands of very-high-status individuals (a high "cognitive Gini coefficient").
Does status actually make people stupid? It's hard to say because I haven't tracked many careers over time. I do have a definite and strong impression, with respect to many high-status individuals, that it would have been a lot easier to have an intelligent conversation with them, if I'd approached them before they made it big. But where does that impression come from, since I haven't actually tracked them over time? (Fundamental question of rationality: What do you think you know and how do you think you know it?) My best guess for why my brain seems to believe this: I know it's possible to have intelligent conversations with smart grad students, and I get the strong impression that high-status people used to be those grad students, but now it's much harder to have intelligent conversations with them than with smart grad students.
Hypotheses:
Did I miss anything important?
Having achieved some small degree of status in certain very limited circles, here's what I do to try to avoid the status-makes-you-stupid effect: