If we want to snoop we could. That goes for the majority here. Most would not get close to being caught doing so unless there were really tight security in place for monitoring this. We don't because most of us are professional enough to know right from wrong and understand the implications of doing such a thing.
You may get a trigger happy junior tech who wants to have a peek at some teachers screen when they first see something like VNC in use. Secure it with passwords and such and wait till the tech is mature enough to handle the responsibility. I think in this day and age a policy is a good idea so that you have some protection should accusations start to fly. Most of us will have a simple understanding in place however, that says we ask before we view and assist.
You can even edit remote desktop to allow unsolicited access if you wish with a few tweaks to GPO's as i have played with this on a test network.
We tend to email the teacher or update the helpdesk requesting access at a certain time with their permission if we feel the job is quicker done this way. If the staff are unhappy with this there are no hard feelings and we will do it in person instead. Never had anyone say no yet.
I understand the principle worrying about such access but i would explain that as an administrator i have full access to all of the files on the system at any time. Junior techs would obviously not have those same rights.
(bet your principle is typing out the BSF plans to remove you all!! Load VNC quick!!!):D:D