You may not agree with the policy or the tools used, but the rules were clear,

OK, if you'll be consistent and agree that using Taro cards to determine who's cheating is normal, if rules say that.

and at this point she has no evidence that she did not use some other Generative AI tool

Your upbringing lacks in some key regards.

It’s just her word against another AI that is trained to detect generated material.

There are (or should be) allowances for the degree of precision where any tool can be trusted. If it is wrong in 1% of cases - then its use is unacceptable. In 0.1% - acceptable only if she doesn't argue it. In 0.01% something - acceptable with some other good evidence.

I'll help you become a bit less of an ape and inform you that an "AI" (or anything based on machine learning) can't be used as a sole detector of anything at all.