I think you are right.
Any approach that is successful on the bully problem will have to tackle the problem from both ends. First, the victims need to learn how not to be victims any more. (that is not to say that it is their fault, but there are things that they can change to make themselves less likely a target. Such as a healthy self esteem, ways you walk and talk, etc).
And second, the bully. The bully is getting something from bullying, and if you can teach them to get that something in a way that is healthy for everybody (including them) it will help them stop bullying.