I just read this whole thread and have a few thoughts.
1. I've generally let my boy handle his own disagreements. I give advice and he can take or leave it.
2. I've stayed out of issues unless they turned dangerous.
For example:
1. A jock, held back a year by his parents so he'd be bigger and more competitive in sports, was harassing my boy. My boy followed the schools preferred method of resolution, it didn't work. What did work was a slug to the shoulder of this bigger boy, in the classroom of an older male teacher. The teacher pretty much turned a blind eye, the older boy was put in his place, and my boy just let it go after that. I don't think they became friends, but neither bugs the other so all's good.
2. Kid on the bus was getting way out of line with harassing my boy. That kid comes from a real bad background. Siblings/parents in/out of juvie/prison, suspenses/expelled from school, other kids injured by this family. My boy tried handling it, but other boy kept escalating. I stepped in and called the transportation office, principal's office, and the bullying hotline. Other kid was warned to stay away from my boy, and was soon kicked off the bus for harassing other kids.
Bottom line, sometimes parents need to stay out of the way, sometimes they need to step in. It's hard to say without personally knowing everyone involved. In general, if there was an unprovoked physical injury I'd see about having assault charges filed, too.