I agree, HMA was just an example to hide the activity from being monitored real-time. Basically there are two aspects to consider: 1) Monitoring online activity while logging and collecting data, 2) Proving illegal activity by collecting trace data left on the computer. By using a VPN service, I am trying to guard against number 1, and of course using a no-logging VPN, as you suggested, helps number 2.
As an additional security measure, in order to leave no trace on the computer, I am using an encrypted home folder and accessing the internet through a Virtual Machine session, which deletes itself once the session is over. The only remnant left on the computer from this activity is the deleted VM, which resides on the encrypted home folder.
No security measure is foolproof, but this makes life a little harder for the IT guys.
The way 960design describes how much he is in control, I get the impression that he sits right behind each student and watches what they do over their shoulder.