Investigation is ok given how much shooting happens. Punishment however is way out of proportion. It was a bad joke. Does not deserve any real punishment except maybe couple of hours in a class that explains why jokes like this are bad.

Inappropriate comments or jokes could easily be handled with parent-teacher intervention and some detention. If it's possibly credible, then reporting it to the police to kick off an investigation is good. It seems that nobody really used their brain in the example given - everyone just trusted some automated system's determination instead of making their own.