I was left to roam the internet freely starting around age 10, saw my fair share of liveleak-style material, lost some sleep over it and grew up into what I like to believe to be a fairly well-adjusted adult who can only shake his head at the sort of things people in his generation experience irrationality-inducing terror over.
I've noticed that my son is the same way, so I tend to be very careful about what he sees. He's definitely more sheltered that some of his peers, but that's based on how he reacts. It's important to know your kids and know how much they can handle.
If a child is afraid of swimming, most teachers would find it reasonable to keep pushing and gradually acclimatise them to the notion rather than give up and say they are just not cut out for it; why would whatever reasoning that underlies this not apply in the case of "disturbing content"?
Mostly porn and torture? I remember that when I was visiting my uncle, and he left me alone playing on his computer. I was poking around, until I found a folder containing video of a group of soldiers beheading a guy.
I didn't sleep well for a week.