Sarcasm does not become you, Christi.
I go to Cozumel every May, and I have for the past... Jeez, is it nearly 30 years now? Whew! Anyway, all I know is that my group never has trouble finding accommodations and is very often occupying the only table in restaurants (except for Kinta, of course). I think that the idea of "high season" is a subjective thing, and what is high season for one business may or may not be for another. Different businesses serve different segments of the tourist population, and they don't necessarily follow the same time signatures.
But IMO, it's kind of a silly argument. Tomayto, tomahto, potayto, potahto, let's call the whole thing off...