The bullied often end up becoming bullies, and in my experience, two children can bully one another, so that is not necessarily a one way experience. In some cases, a smaller child can even bully a taller one, although an adult would think that was unlikely.
While it is possible to stamp out physical bullying, psychological and verbal bullying are near impossible to eliminate, and so any sizable school which denies having it is lying. It is a matter of degree, and how they handle it.
