yes, i guess you are right about the "student" and "teacher" crap, but, joe certainly shouldn't be credtied with teaching vai everything he knows, i don't think he was far ahead of vai, at the time.
i read about this somewhere, and it is not like vai spent years "studying" under joe. i think it was just a few lessons in the beginning, then some jamming.....i think vai is far more advanced and creative than satriani, but that's just my opinion.