Sisko could point it out to Beverly. "Yes, he's the captain, Doctor, but as Starfleet feared, he's acting on what happened to him. Would he ordinarily act like this or would he give up the Enterprise?" If her answer to the question is "give up the Enterprise," then he can logically point out that maybe Picard isn't fit for command. As for the question of them not knowing him, unless the command crew acts as they did in "Chain of Command, Parts I and II," they may listen to Sisko.