Debate moderators should not have to fact check as it's up to the opposing debater to catch and call out the other's lies. Moderators have a tough enough job to keep the debaters within the time parameters and stay on topic. Interviewers, however, (as with Matt Lauer) have a responsibility to make sure the facts are known and not allow a liar to simply brush off the facts during the interview. I think Lester Holt did a fine job.