Well, they are magicians. Cut 'em some slack.
Just look at this:
Tim’s device is Vermeer’s device! I have no doubt. Tim can give you all the doubt you want, but I have none.
It's pretty clear that we're not dealing with rational people here. Which is fine, as they're entertainers, selling to an audience composed of irrational people.
This bit is particularly telling:
The idea of an amateur coming in and understanding things experts can’t see—that’s a very American kind of plotline.
The amateur, outsider, the autodidact -- if they're only smart and clever enough -- can outwit or otherwise make a major contribution to a field they're interested in. It's their very standing as an uneducated amateur that imbibes them with insight far beyond that of the average expert.
It seems silly at first, but there's a lot of money to be made pandering to the egos of the scientifically illiterate science cheerleaders.
So relax. Their viewers don't care about silly details. The magicians don't care either. The audience doesn't want to question what they're told, and the performers don't want to bother fact-checking everything. It's just not that important to them.