Of course they cut water weight, jesus christ, I've seen them do it. How else do you think they put on 20 pounds overnight other than rehydrating?
It's very normal for pro boxers to run in sweat suits, and use saunas. They've been doing it before MMA even existed.
Again, I don't know how this myth started, but if you don't know what you're talking about, it's best to not spout bullshit and spread misinformation.
Boxers absolutely cut water weight and have been doing so for decades.
If you've never seen a drained looking boxer at a weigh in, you simply don't watch boxing. A lot of boxing fans even wait till the weigh in before placing bets in case one of them looks overly drained at the weigh in.