5th dnd – Can the Magic Weapon spell be cast on a natural weapon?

From what I understand, natural weapons are considered weapons, for example for the purpose of improved Divine Smite's ability (see discussion here).

Again, according to Jeremy Crawford it is not possible to cast the Magic Weapon spell on a Natural Weapon:

The spell of the magic weapon targets the weapons (PH 146-49), not the body parts.

It makes me very confused. Is a natural weapon a weapon or not ?!

More precisely, can the magic weapon spell being thrown on a natural weapon?