I'm the technology manager at a school but beholden to a larger "Management" company for a lot of my processes. In our case, we can't afford to issue laptops or tablets or Chromebooks to students, however it is absolutely true that we have access to everything everybody does on school computers. This includes students and to some portion, teachers. We tell everybody straight out with big, bold text that we have access, but people do stuff anyway.
Tuesday, a new employee got onto his computer for the first time and within five minutes I had an alert that he'd downloaded a "flash-installer.exe" infection when he'd managed to find a porn site that wasn't blocked by our filter. He was fired within five minutes, because a trace showed that it was obvious intent, not accident.
On the student side of things, we are required by law to report things, and it is not often thankfully, but we have been alerted by monitoring software that a student was being solicited by an adult for illegal activities. The student logged into their personal GMail account from school and typed in a reply. All captured and monitored and observed. More common is catching online bullying.
In general, it does show just how much access we have and why we have such extremely strong language in our alerts to say "Yes, we can see EVERYTHING." Also one of the reasons we are reluctant to issue take-home equipment to students because of blasted cameras and no desire to even tempt anybody.