Personally speaking, I don't believe the advice you offered in your OP will always work. Let me tell you a story of a specific bullying incident that happened to me when I was 18 years old, so you will understand why I disagree with your advice in the OP.
My older brother bullied me and pushed me around for years, but that came to a dead stop the day I finally stood up to him. It was shortly before I moved out of the house when I was 18 years old. He was doing his usual taunting, and he would usually punch me on the arm whenever he walked by me. Of course, our parents knew, but they didn't care, and they never tried to stop him. Well, my brother sat down on the back of the couch after he had just pushed me when I walked by him in the hallway. I finally snapped, and I pushed him backwards off of that couch with every ounce of the 95 pounds I had in my body. He hit the floor with a loud thump, and after a few seconds, he sat up. He was in shock, and so were our parents. They stood nearby with their mouths wide open. My brother finally stood up and took a couple of steps towards me as if he was going to lunge at me. I stood my ground with my fists clenched, and I told him point-blank, "Go ahead! If you lay another hand on me, I'll call the police! I'll press charges against you, and there's not a damn thing mom and dad can do about it!" He looked over at my dad, and my dad said, "She's right!" My brother never laid a hand on me again. My abusive mother even backed off, and she never laid a hand on me again, either.
As you can see, ignoring the people in my life who bullied me never worked because none of them backed down whenever I tried to ignore them. They only stopped pushing me around when I finally stood up to them and fought back. My decision to confront these people did lead to a couple of physical confrontations, but I learned that I'm a stronger person than I thought I was.
As I shared in my personal story, I grew up in an abusive home where I was physically and psychologically abused. I was also bullied by other kids for years while I was in school. There was no escape for me. I learned years later that it was common knowledge that I was being abused and bullied, but no one tried to help me. My extended family, the neighbors, my teachers, and other adults in the town we lived in when I was a child all knew that I was severely abused at home. They all knew I was also being bullied in school.
Long story short, it wasn't until I stood up for myself that the bullying stopped. I finally started to stand up for myself in school and I confronted the bullies. The bullies stopped trying to push me around when I fought back. The physical abuse I suffered for years at home completely stopped when I finally stood up for myself and fought back. I moved out of the house shortly after I turned 18. I moved out to get away from my family, and to make sure that my brother and mother wouldn't physically abuse me anymore.
