Has anyone else misremembered that lucky hit was in Shenmue I?

When this game first came out, I watched my older brother play it on the Dreamcast. I never played it Shenmue until recently, but I just finished the first game. The game was a nostalgia trip, and I remembered plenty of elements accurately from watching the game: the english dub, gacha, forklift races, etc.

However, I distinctly remember lucky hit being a minigame in the first game. I acknowledge that - it this parallel universe, at least - lucky hit seems to only be in II and III. The fact that I remember lucky hit is kinda tripping me out. I swear I remember seeing my brother play lucky hit in game somewhere in Dobuita.

I don't think I'm conflating I and II either. My family had a Dreamcast, never had an original Xbox or spent a lot of time with it, and I'm in the U.S. I think that means that I would've never seen II, and therefore lucky hit, unless it was on the Xbox, but I'm similarly sure that's not the case.

Has anyone else had this memory? Did adding lucky hit, or not, to Shenmue I come down to a coin flip by Yu Suzuki that came out differently in the mirror universe that I unknowingly come from?