Are AI detectors accurate enough for teachers to rely on?

Here is how I got there. Our school gave teachers access to a detector this term. The first batch of essays I ran gave me a spread of scores that did not match what I know about the students. One of my strongest writers, who drafts in class and whose voice I know well, came back with a high "AI" percentage on a paragraph that is plainly hers. A weaker essay with a few oddly polished sentences scored low. Two data points prove nothing, but they were enough to make me stop treating the number as a fact.

What I have tried since:

• Comparing the flagged essay with in-class writing from the same student
• Asking the student to talk me through the argument and where a particular source came from
• Looking at the document history where the student used a shared document

What I still want to know:

1. Is there any published evidence on how often these tools are wrong, from the companies themselves or from independent work?
2. If a vendor says its false positive rate is low, what does that mean for a class of 30 where most students did nothing wrong?
3. What would a fair process look like when a score and a student's account disagree?

I am not looking for a ban or a blessing. I want to know what a careful teacher should do with the number once it is on the screen.