I'd just like to add a few things.
1) this guy sounds like a typical ego-inflated nerd who doesn't really know enough about computers to get a job doing challenging work, and has snagged an easy gig running a small college network. Any computer literate people, especially people who are able to use systems he's not familiar with, are bound to be extremely threatening to him, and he has real power, so tread lightly.
2) I am almost certain that he can't determine what software you are running on your private system unless you give him an account. So his claim that he'll know if you're not running anti-viral software is a bluff.
3) He can scan your system to determine what ports you have open, and, unless you take measures to prevent it, he will also be able to determine what version of OS X you're running. However, if you're up-to-date and not running P2P software that opens ports he's looking for, there should be no problem here.
4) Do NOT install Norton Antivirus on your mac. It's a completely bug-infested heap of garbage and it will almost certainly screw up your machine. It's also inordinately difficult to un-install. Symantec has discontinued its development besides. If you feel compelled to run some anti-viral software, find something else (virex comes to mind).
And finally, our system admins here have made similar draconian rules, and all of us mac users just ignore 'em. They can't see what software you're running and they have no right to invade your privacy. Let 'em port-scan you, and spend their time dealing with the endless catastrophes that befall the windows users.
Cheers