They can do whatever they want, because if you refuse you will be considered to be "interfering with a flight crew" or something like that. I mean, in this case, the passenger could have denied having a passport, since it's not a document that's needed on a domestic flight. But I'm sure the FA would have simply asked for a drivers license instead.

Nice to see in this case the passenger was not charged and was allowed to go on her way, but sheesh.