The whole "nut" thing gets clear down to telling the public if ANYnut product of any sort MAY have come in contact with other foods. This has become a common "Posted Warning" in many food establishments. However, to ban nuts and not the other products like P-B and peanut oil makes no sense whatsoever to me.
For me, part of the issue here is talking to kids in general about this and other things. Many kids, not just Autistic children, take everything said by authority figures to heart and in most cases that's okay. The problem with kids like Tris and Villain's daughter is that once told something like this it is nigh ass next to impossible to convince them otherwise!