As much as parents have to take some responsibility, whether they can or not depends on two things - firstly they have to find out, and secondly they have to be able to do something about it. I was able to keep, for the most part, how I was feeling from my parents for ages. They could have pushed and probed for ages and got nowhere, although in part things were helped by being actually separated for much of the year.
And even if they had found out, fact is that I know my way round the internet and computers far better than either of my parents put together. Short of pulling the plug on the whole thing, which would have cut my parents off as well, they wouldn't have been able to stop me going where I wanted if I was determined enough. There's a story that one mother tried to stop her son going on the internet by deleting the browser icon rather than the program itself! While that's probably at the extreme lower end of parents' ability to use the internet, in some ways my parents aren't all that much better.
So it comes down to two problems: that the parents may not have found out, or been able to, and that even if they had found out they may not have been able to do much about it. In both cases the problem is the bullying itself.