The data being presented here is not anywhere close to the level needed to invalidate the claim that fatigue affects performance. It's anecdotal. But that's not Waterhead's fault. Data was demanded of him, and he's doing his best with available resources.
Mick Cronin is most likely not relying on data. He's probably relying on intuition. Waterhead called it superstition, which I would say is an exaggeration. But I get his point, which is there isn't any scientific evidence to support the idea that sitting a player for an extra 5 minutes in one game will improve his performance in subsequent games. There was an NBA study done last year on sitting out full games, which came to the conclusion:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5637977/
But even that study isn't well controlled and has a relatively small sample size. This is an issue that is unlikely to be resolved using data. So I would recommend not digging into your position, rather allowing that someone else's opinion is valid, even if it's not backed by evidence.