With no knowledge about how i goes for babies, the question would be how a 2~3 month allergic kid [0] would react to peanuts, including when not directly ingested. If it had adverse effects it would go along the line of what parent is describing.
[0] can kids that age already be allergic to peanuts ?
Allergies are a subject I need to know a lot more about, so sadly at this point I don't have an explanation for anything.
I don't see how any of what I said is either insistant or limiting to a single cause.
I was facetiously pointing out that a population where everyone eats peanuts at a young age is likely to be allergy-free if only due to the fact that those with peanut allergies would die, and therefore would no longer be allergic to peanuts. A naive analysis of the data could lead to a conclusion that eating peanuts at a young age causes a favorable change in allergy outcomes later in life.