You seem to be conflating a few things:
IANAL, but my understanding of the national park regulations are that only boats with park permits are allowed to use the park for commercial purposes...and yes, if you're paying someone to use their boat, that's a commercial charter -- the word "private" in "private charter vessel" simply means that the paying customer isn't sharing the boat with strangers.
Separately, the CONAP regulations seem to state that all visitors must pay the fee, regardless of the ownership of the vessel (subject to exceptions for senior citizens, the disabled, etc).
https://descubreanp.conanp.gob.mx/swb/conanp/ANP?suri=4