There are people who are allergic enough that they need that strict a rule. They are few and far between.
That said, facility warnings are 100% optional. The school doesn't know that something is from a nut free facility because they manufacturers don't have to say that and I HIGHLY doubt that every single snack coming in is from a PN free facility. I would not pack anything with nuts in it but "processed in" free school- I doubt that is happening at all.
The school won't tell you if there is an allergic child in the school so I would set up an area where your kid eats slightly away from others (but not too removed) and call it a day. I would also make sure your child knows there is no sharing. Setting it up this way, if there is a child with a severe enough nut allergy that it would be an issue, they can park that kiddo on the other side of the table or whatever so BOTH kids are safe!