Goldeen/Seaking & Waterfall

[Greninjaman]

Let's say you have one of these and it learns Waterfall. Since Waterfall is an HM in gens 2-6, does that mean that once it learns the move via level up, it can never unlearn it unless you go to the move deleter?

 

[Unovia]

Let's say you have one of these and it learns Waterfall. Since Waterfall is an HM in gens 2-6, does that mean that once it learns the move via level up, it can never unlearn it unless you go to the move deleter?

The bit of research I have done suggests that unfortunately, Pokemon that naturally learn HMs cannot forget them, as the game does not differentiate how the Pokemon learned the HM, whether by Level Up or not.