but peanuts are one of the few that are so severe that simply breathing it in can bring about a reaction. or touching a door handle after someone else with peanuts on their hands has touched it.
there are other allergies, but I haven't come across others that can be quite so easy to affect people.
so, yes, for that one child, it pretty much is important that no-one brings peanuts to school. even that won't really make them safe - one kid having a pb sandwich for breakfast, could walk past them & breathe & trigger a reaction.
I would hope that if another child had a similarly severe allergy, then the school would follow the medical advice provided on the issue.
I teach older kids, and the other day one child suddenly got up & moved, then said 'he's having a peanut bar, I know I can't sit next to it'. IF she were younger, she might have sat there for longer, and ended up in hospital. Thank goodness she's sensible, and knows which brands trigger a reaction, just from a class mate opening up a packet.