Going back to "The Naked Now" - there isn't anything that specifically contradicts the past "Starship Class" designation. Unless you also want to say Kirk was never an Admiral as well?
But that isn't what the argument is about. You have someone saying that those that use Constitution-class are somehow spitting on the graves of those who worked on the show and those that are the holy defenders of canon. Even though some of those folks were around and approved of it also being known by that class name as well.
No one made Constitution class up out of thin air to piss off the die-hards.
When you frame it that way, then yes their argument is on the extreme end and I do not agree with that.