We have no way of knowing how much control Carey has over the product. The show is obviously taped and who knows what got left on the cutting room floor.
I’m not accusing Carey of liberal bias as much as I am accusing the show itself of being biased. I don’t expect the game show to resemble the Half Hour News Hour. I’m just expecting a game show to be politically neutral, particularly in the season premiere, and it was clearly not.
That's what I gathered from this bit you mentioned:
One polled question was (paraphrasing) "If you were to get into a shooting duel with Dick Cheney, would you win?"Carey amplifies the question by saying "You know, he's not very well-liked."
Cheney's apparently not well liked by the staff either.