if a moderator know that an obvious lie has been said, then he or she should call the candidate out on it. period. if they can't do that, then they should at the very least ask follow up questions 9which they do already) & have the candidate 'expand' on the lie, so they can dig an even deeper hole.
Followup questions are appropriate for clarification, but moderators should not contradict a candidate with their own opinions or beliefs, which may themselves be factually inaccurate. Did you see the recent episode of
Jeopardy! where the guest MSM talking heads couldn't answer simple questions about politics and government? Candy Crowley isn't the only self-assured idiot "journalist" out there.