A very good point. If people are allergic to peanuts, then they would possibly be allergic to other members of the pea family. I've never heard of anyone being allergic to peas.
Your modern domesticated pea has been bread to not produce those and other alkyloids over thousands of years.
If they were allergic to peanuts then alfalfa, clover, peas, beans, lentils, lupins, mesquite, and carob would also pose a problem. Parents need to get a grip. Either the kid is acting on cue or there is something else going on.