Perhaps the school had a rule against installing non-authorized software on school computers. In a virus crazy world this would not be an unreasonable request. (I am not opining on MIE vs. Firefox - I think the best browser is the one you enjoy using the most.)
Your scenario assumes the student accounts have admin privileges. If IT gave the kids admin rights and is now mad because he’s using Firefox instead of IE, sounds like he’s more qualified than they are.