I think you misread that comment. She stated that her kid would not tell her that she IS bullying (not BEING bullied).
Any sort of meaningful conversation with my kid about it would likely devolve into a childish argument where the defense is "No, I'm not. It's the other kids."
You're faced with two choices here. On one side, you can back your kid. On the other, you can think that you're likely not getting the full story and that something really is going on.
My child, in particular, has a real problem with shifting blame. You need to have a read on your children so that you can properly judge for yourself what's going on. Bullying is not ok and your kids need to know that it's going to be no nonsense when it comes to bullying.
It is the adults who have the power to create an an environment of trust. Not the kids.
Consider that it is possible to be both bullied and a bully at the same time, and that while bullying is a terrible behavior that cannot be condoned, a bully may not want to be a bully and may need help to stop other than simply being blamed.
I don't think I've ever encountered, in real life or media, a child coming clean with their parents about harassing and hurting other people without some outside pressure (aka other parents or the school getting involved)
I think that kids do experience shame when they hurt others, and will confide in people they trust, if they have such a person.
I have witnessed this. Obviously if they've developed a serious pattern of bullying then it's going to be a lot harder, but having kids have someone they can confide mistakes in before that happens is part of how we can prevent it from developing.