Sorry, I'm clearly sleepy.
Actually it's not even an exploit, it's a mechanic introduced in Sword and Shield.
As long as your mon has space for learning moves, and placed into the breeder, it'll learn the possible egg moves from it's partner (provided it's the same species and opposite gender) at the breeder.
So yeah, past gen Vulpix should be capable of Memento. (via the relearn transfer mechanic)
But even so, learning a "relearn move" from the partner, won't go into the Relearn move slot of the mon itself.
@Kaphotics this is the real error:
(my bred Ninetales from the VC era, with Toxic learned in Gen 7, then Memento passed to it in Gen 8 )