They’re both correct, but TachyonTele is more correct about the history of the game as it started development in the beginning. But it’s also true that SMB2 in USA was made by reskinning Doki Doki Panic because the real SMB2 was deemed too hard for western players.
And I’m not surprised a video game history class wouldn’t know about internal development design decisions and only knew about what was stated publicly in interviews over and over etc.