Mediators don't provide the disputants with answers. They don't tell anyone what to do, or force anyone to apologize. They certainly don't punish. They don't report back to the teacher or the principal. They just carry out the process and complete some simple, confidential report forms for the mediation coordinator.
Mediation is a voluntary alternative to traditionally punitive consequences.
We use it only when the offense is serious enough that, if ignored, it would seem about to create a referral, but it hasn't yet crossed that line. In a well-planned and implemented program, most disputants will come up with workable settlements. That doesn't mean perfect. It means that the disputants felt that the process was fair and reasonable, and that the solutions work for them. Some schools allow the option of mediation between adults and students when both parties are willing, and when the issue at hand is not a serious breach of school policy.