What are the chances that a teenage boy would brag about having sex with the exceptionally beautiful teacher who most of his classmates only fantasize about? [My guess - close to 100%, but do these women know that?]
I would guess he would have enough sense to not brag while he was getting it, but WOULD brag after it was over.
These teachers are stupid. Do it once, and the student has blackmail material. I would not be surprised if a student secretly set up a video recorder on the first tryst, and told the teacher afterwards "You're going to do what I want, or the video gets sent to every administrator in the school system".