This same issue is raising its head in the presidential debates where journalists whose job should be informing the public on the facts are being picked to moderate debates which need to be fair competitions. This puts the journalist moderators in a very similar type of conflict of interest. Should they be fair and not be expected to do the other side’s work for them or should they stick to their moral duty as journalists? The solution in this case is simple, we need to stop asking journalists to mediate these debates and instead ask retired judges or some other neutral party schooled in debating. It should also be explicitly stated in the rules that it is never the moderator’s role to identify the facts or misrepresentations.
In the class situation above I simply could not let the falsehood go so I did tell the class about the one off experiment, the online shenanigans and that the point was wrong, but only after the debate was over and the outcome decided. I also asked the class to consider the rhetorical techniques that our super debater skillfully employed to persuade them. Unfortunately I was still taken to task by one student in the end of semester surveys for “calling out” the star debater to the class. I don't know what else I could have done. Sometimes you just can’t win.