Being late for class or mouthing off to a teacher are facts, not up for debate. Students get punished for that all time in sports. I was more of a basketball guy in hs but our coaches did the same thing so not disagreeing there.
I don’t agree with punishing someone based on a rumor or some he said/she said. Anyone can accuse anyone of anything or start any rumor.
If it turns out there’s evidence of wrongdoing, I’m all for appropriate punishment - whatever that may be.