I agree with you that some parents exaggerate their child's allergy but I think there is another reason: "better safe than sorry" parenting. Little Johnny is known to be allergic to eating peanuts so we won't let him touch them, or inhale the dust, or sit next to a child who is eating PB in the lunchroom, or fly on a plane that had peanuts, etc, etc ... all because it's better to be safe than sorry.
Instead of admitting that the known allergy is only for ingested peanuts the parents make up wild exaggerated claims of deadly allergies to make everyone else come in line with their thinking. In my last "peanuts on a airplane" discussion there was a poster who said that her child was
so allergic that she had a severe reaction from someone opening and eating a bag of peanuts at a baseball game 6-7 rows behind them! When pressed on it, it turns out that the child had a reaction from peanut residue on the seat ... not from what someone did 25 feet away. There is an element to the boy crying wolf, if you KWIM.
I don't mean to discount peanut allergies. Some can be quite severe and I feel for the parents of the children. It must be terrifying

. My kid is a PB lover but we try not to pack peanut products when we fly just in case we can't eat them. Better safe than sorry

(just kidding, I had to say that!) It's not a big deal as long as I think in advance. On the same note, I also think that the parents of PA kids need to think in advance too. If my kid was allergic I wouldn't consider flying with an airline that routinely serves peanuts ... no matter how many FF miles I had, how cheap the flight was or if I had to take multiple connections. My child's heath and well being is worth it.