I had period where I obsessively read too much about those cases. That was pattern I have seen. The first media usually contained such speculation, the later reports did not really confirmed it. What those contained were stories of other kids being attacked by them or afraid of them.
Show me three whose lives show them being bullying victims striking back. Go to read a biography of pretty much any popular one and you find raising levels of aggression toward people around. I have yet to see a ONE that would be a bullying victim lashing back.
Really, show me some that were primary bullying victims string back.
Adam Lanza and Elliot Rogers had both mental health issues and family that allowed them to isolate themselves. Adam Lanza mom was reported to be afraid of him before the end and basically in abusive relationship with him (where he was the abusers) before being killed. In case of Nikolas Jacob Cruz, you see volatile boy threatening and attacking others including a girl that school assigned to tutor him. She stopped because he was bullying her. He WAS ostracized and lonely as a results ... but that is the kids avoiding the bully who mistreats them rather then him anything else. He had host of mental health problems for sure too.