Surely this is trivial to refute? The professor just needs to have his own text that he generated using AI. When your website says it's not AI... then it's curtains I guess?
The student just needs to find a pre-2022 article that is mistakenly marked as AI by the professor's detector.
It's harder but probably not that hard.
Ideally, what the student should probably do is get ahold of as much of the professors own work as possible and feed it through the detector. While pre-AI work might be best for proving that the site can't possibly be reliable, post-AI work is probably better for convincing the professor that the consequences of treating the site as reliable are bad for him.
By the time a professor is this engaged and thinking this logically, the student has already won.
It would be, if the professors website wouldn't suffer from false negatives as well. Which it most certainly will.