Angry wasp trap is more or less the first thing that came to mind as a solution to the desk moving problem. I mean, the only real limitation is that the trap has to be setup in such a way that it looks like the person triggering it was the one who was setting it up, right?
Hrmmmm. Actually, thinking it further, the trap could be of an arbitrary complexity if you consider multiple people being involved in the bullying. Scapegoat A would be blamed for setting the trap, while scapegoat B would be blamed for triggering the trap while trying to move it. As long as the groundwork for laying idea of blame elsewhere was done beforehand, it would be easy to blame the bullies for hurting each other. The only real requirement is that the bullying be predictable, seeing as these are japanese high school students they'll confine their bullying to 1) shunning 2) destroying school supplies 3) hiding desks 4) hiding/destroying gym clothes 5) hiding/destroying shoes.
Too much thinking?