Well, if the “vaccine passport” is going to be effective, they will crosscheck names with the lot numbers. If your name isn’t on the list for the lot you are claiming on your card, you don’t get a passport.
Haven’t you been paying attention? The only vaccine ID there is at present in most places, and all I’ve been talking about, is a simple handwritten card. If they get to some kind of more stringent requirements, with cross-checking people’s medical information against vaccine-lot databases, then a good fake will be much more difficult. If it stays like it is currently, I don’t see some airline clerk running every passenger through multiple databases. They’ll just glance at the card.