It doesn't even have to be a serious allergy - as I've gotten older I've realized that a lot of foods I "didn't like" for no reason as a kid actually made my mouth burn or my teeth hurt or made my tummy mildly upset, I'd just internalized that it meant I just "didn't like them" because that's what the grownups said.

I would suggest teaching the kid to say, "I don't want to eat that, it makes me feel bad" instead. Covers a multitude of reasons, harder to ignore but also not minimizing actual anaphylaxis, invites adults to help them articulate real food issues.