Knew it!
Well, the way chapter 29 ended made it pretty clear. It's not that she was confident she wouldn't fail regardless of whether the curse was real. She wanted it to be real, because it was her only way out.
There doesn't seem to be anything wrong with the university itself, since she doesn't think twice about helping Hajime to test into it. She just had to be sure Hajime had at least a chance of making it, and he proved that by winning the bet.
My (highly original and unconventional) guess would be there is already a fiancé candidate in the picture, or rather several, all from very prestigious backgrounds, and they all have in common that they will attend this specific university. She figures she can sneak him into the lineup somehow on a technicality, even if he's definitely not what the patriarch had in mind, and make that her hill to die on.