I find the extremes of sensitivity and insensitivity among the comments here.
Bullying is a serious issue, bordering on or crossing the border of pikuach nefesh all too often. Every single yeshiva must have training for all staff, teachers, administrators, clerical staff, etc. And the policies for how to deal with every situation must be in place. For a serious, serial bully, experience suggests that measures short of arrest are futile. Many other cases are not as advanced as that, but cannot be allowed to pass lightly. The smack on the wrist of the bully just contributes to the anger that gets dumped on the victim(s), and enables further violations.
Discipline is rarely a preferred modality in chinuch. But it is the only one with an ounce of value in bullying. Bullies do not stop until the pain they incur themselves is greater than the glee from inflicting pain on others. I have heard of some old school mechanchim giving a punishment of writing lines to a bully, or similar gestures. What a complete waste. There was a chinuch moment that was scuttled. It is not rare that a bully is from a family that has some form of clout with the yeshiva, money, stature, family connection to the hanhala, etc. Protecting the bully here is as disgusting and abhorrent as harboring a pedophile who victimizes kids.
Every case must be assessed on its own merits. But bullying is rarely fabricated. And any school that supervises its students properly can have evidence in most cases that do lack the types of injuries that cab be detected visually. Are students supervised during recess? How about before and after school? Do students feel safe enough to bring such reports to the administration?
Why look to protect a school before looking to keep a child safe?