No, not true. The parents of bullies are usually bullies themselves. The solution is to draw a hard line and say, I will take this so far you won't want to go where it ends up.

When I was a kid I got pushed so far that one day, when a bully stole my stocking cap for the 50th time and was going to dunk it in a cold puddle along the curbside I ran up and pushed him into the busy street's moving traffic. He was totally shocked - at that moment he realized I would now do anything to stop him. He never touched me from that day forward.