Did I just get a bad agent at ZRH or did I misread the rules?

Flew US-ZRH-FRA-Middle East so my Schengen entry was via ZRH. UA couldn't print my onward boarding passes so I had to go to the transfer desk upon arrival at ZRH. I gave her my itinerary and asked her for BPs. Besides the fact that she said, "You're supposed to do this in Terminal A but I'll make an exception for you" she then insisted I had to show her my vaccination record to enter Switzerland because I'm an American. I didn't think nationality mattered at all (unless maybe if you're from China)? I told her there are no requirements any longer to enter CH but she insisted and wouldn't print my BPs until I showed her my vaccine card. I always travel with it so I'm glad I had it because all of the other countries I'm entering on this trip have zero requirements.

Was she wrong or am I wrong?

-RM