Schools policing students
You're not missing anything at all. It is not the right or obligation of the school to police students off school property. School administrators aren't cops, and obviously don't know enough about policing to understand privacy rights and civil liberties. A student can be suspended, expelled, etc. for being charged with illegal activity, but only when charged through the proper legal channels - i.e. charged, tried, and convicted.
Public schools in the US have been increasingly pushing this line and it's getting scary. What is considered "inappropriate" by a public school is technically held to the same standard as law, being only what is illegal. More and more cases of children being expelled for personal behaviors that fall within the bounds of legality are cropping up. Recently a teenage girl was charged as a sex offender after her school found out she sent a picture of herself in a bra to a male colleague who was also a minor.