This is a link to a video about a teacher in Kentucky who has been accused of having sex with a 16-year-old student. When the rumors started circulating around the school, the teacher immediately went to school officials and reported it. The teacher was suspended, and then arrested. Even though there is absolutely no physical proof or even witnesses that anything had happened.
After the school looked into the rumors, and the rumors were determined to be false based on the simple fact that the student involved told them that there was no sexual relationship of any kind, the police and prosecutors arrested and charged the teacher.
It certainly does sound like this is a case of a false allegation.
The kicker in all of this? The teacher is female, the student male.