You do really need to make a stand on this. Personally, I would offer a test or demonstration where you write a paper in a place where you can be assured to not be using an AI, and have them check the false-positive rate to show the vendor they have is bad. Short of that, you’re really talking about pushback on an administration that clearly has only mediocre ideas, and is willing to let students suffer the brunt of their bad decision-making until you make it a problem for them.

Students should have a way to seek real recourse about this. Use it now and use it early to establish a record of receiving false positives, Otherwise you risk some professor later really causing problems with a 5% false positive rate and it being a huge problem for you.