School administrators have much less power than you might think. In public type school systems they're left answering to a lengthy hierarchy which doesn't even end at the superintendent, because they in turn are often beholden to various bureaucrats. And in private schools of significant size, there are usually investors or other monetary types at the top, but well out of sight.

In either case, the people at the top tend to know very little about education and they're often the source of really stupid policies that sound decent only if you know nothing about schools and/or are incapable of seeing second order effects, such as with zero tolerance.

In any case, the admins there probably wished the OP would have punched the bully back. That's what stops bullying, and oddly enough often even results in friends being made. At least among boys - girls that get physical with each other will hold a death grudge til the end of time, but also get physical far less often as a balance to that.