But they're also in the business of responding to search with facts.

YouTube is a strange platform in that respect, but if someone searching for the moon landing gets a conspiracy video in the results because it's popular I don't see anything wrong with YouTube including a snippet of verified information that relates to the query.

For them to be wrong, they'd have to have an opinion. Why do you think people watching a video like this have a strong opinion one way the other? Maybe they don't and are just looking around.