Fair Use Policy and legal obligation

Fair use policies have been in use for internet access for as long as I can remember. When I was in middle school I remember having to sign a fair use policy with my parents in order to use the internet in school. I also recall having to do this to use library computers as a child and in highschool for the same reason. My understanding of fair use policies is that they are in place to protect school and other organization from any actions that students take on school computers and to also lay out the ground rules for computer/internet use. But what happens if a students partakes in illegal actions online while at school? If they signed a fair use policy does it mean that the parents are held legally responsible?