The the dean, and everyone else, think a super strictly supervised exam would be the worst alternative for Deborah, when in reality it would be the best for her, and thus she would be more than pleased to go through it. After all, her cards in petty politics are few, basically only her background, as her reputation works against her, and she hasn't really got that many meaningful contacts/allies outside of her family. Even in her family her friends are limited and reputation bad. So, if she had to prove her innocence by recruiting allies and convincing people through talk, she could be out of luck.