Huh, sounds like they're using Netreg or an appliance that would do the same thing.
Even still, those types of programs/devices are flexible enough to allow game consoles, etc.
As for making your network "faster", yeah...they're feeding you a line of total BS. The admins there are either very foolish, or extremely paranoid. I'm not going to get into the details of network engineering, but really, a univeristy has no excuse to block that kind of legitimate traffic. The reason they have you login to the network is to cut down on potential problems like an arp storm or propogating network virus. But then again, thats why they have IDS/IPS's, and subnetted campuses. Sigh...I feel for you. There'd be a riot here if we did something like that.
I suppose theres some trickery you could use to get past your University's security, but I really think that would put you at serious risk for losing your network connection altogether if your campus is that strict. If you don't mind saying, which school is this? This is the first time I've heard of a major college doing something like that.
Do they have a lot of restrictions? How do they deal with students that bring routers with them that allow NAT, or are they outright banned? They MUST make exceptions for students with Linux boxes or Macs. The netreg should be able to determine OS as well and base its "access criteria" on the OS.
The only thing I can think of that might work without setting off too many flags would be to use your PC as a network bridge for the 360. BUT, theres the potential that if you mess things up and create a network loop, your port will shut itself down before you can cause an outage. If the admins weren't smart enough to create traps for that...well, you might take out your floor or building's network connections while the loop exists.