Eh, I'm willing to trust people to describe their own health issues. Sometimes we shorthand—my partner says "Can't have dairy, can't have gluten, can't have spicy things" to restaurant waiters because that's simpler than explaining the nuances of their physical and psychological reactions. Plenty of people say "allergy" when they don't have a literal allergy because if you say "sensitivity" you aren't believed or taken seriously.

What matters to me in this letter, much more than how they phrase it, is that there are things they can't, won't, or don't eat, they've asked not to receive those things as gifts, and they receive them anyway. That's not okay no matter what word they put on the reason for can't-won't-don't.