I've run my Balance from brand new right through to level 73 alongside my best friend's Fire Character. We've been within 1000 exp the entire way, and most of that difference has come from him getting the final hit in fights. I don't think there's any difference in School Spell Exp, as we've both stayed so close throughout.
I'd say your ice friend is incorrect as to the exp he gained. You should look the spell and quest up on central, and see if he's right.