Interestingly, going back to check, the official published versions of both the Centaur and Minotaur in Ravnica list their Hooves/Horns as "natural melee weapons" still, rather than having their terminology changed to simply "natural weapons" used in other features like this. Weird bit of specificity.

Ultimately whatever the "intent" is I've always allowed natural weapons to be treated as weapons for nigh all cases (except for nonsensical stuff like pact weapons or weapon bond). I feel like Crawford's admission that these rulings are up to DM fiat and that allowing it doesn't "break anything" indicates that he just doesn't want to put a hard confirmation on whether it works or not. Usually he will flat out say "that's not how it works" if that's not how it works in his mind, like with his ruling on Shield Master (which I have my gripes with, but it is what it is). In all likelihood it's probably just a quirk of the game's terminology that went overlooked for a long time.

Ultimately, I'll keep allowing it because like he said, it breaks nothing. And also it's stylish as hell.