If the wife fought her dismissal up to the level of the university vice president, I suspect shyness isn't one of her problems. I suspect "doesn't deal with conflict" means "would act like an entitled jerk and screw up any chance of getting back in the program".
But I think you handled it well. A useful phrase for similar occurrences could be "I can't tell you that, it's against the law", repeated. That emphasizes that it's not you who is denying his request, it's legal requirements.