This must get pretty frustrating for MIT students...
Now, all the other crap-- course scheduling, grades, classwork --is likely not living on the same server. Many of these things aren't even hosted inside the school's network but provided by some outside company.
E.G. if they had blackboard (course docs, homework, etc.) on blackboard.mit.edu then that would be hosed right now, wouldn't it?
I suppose it could be a problem if you're not on campus; or if any third-party services are not using their own domains (e.g. mit.blackboard.com)
Also, ASP/SAAS companies in the .edu space often use a DNS name that is part of the school's domain in their model.