I think she would have the talents and wits for a double degree. There's no question of her qualification for being a Doctor, yet she has also mastered her summoned demon practically perfectly.
Considering the principal himself is a one big farce, I wouldn't think overly deeply about it.
Other than that, I'm a little disappointed Shiemi didn't already notice Rin's true nature. But maybe it would have been too early and I suppose the author wants to utilize a few close encounters.
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