It probably resembles the thing we've noticed with previous generations, where you can't trade or release your last Pokemon with a given HM move or the ability to learn that move. The programmers do that so that you won't get totally stuck during gameplay.
As long as you have other Pokemon with the same HM moves in the RSE games, though, I don't think you'll have a problem. Can't say for certain, but that's what it seems like given past observations. (Alternatively, you could always go to the Move Deleter and have him work his magic, although that's a bit of a hassle.)