It's a tricky one because of the nature of the net. Let's say we have three kids: Timmy, Jimmy and Harry.

Timmy starts looking up "tits", because Timmy loves titties. He's curious, and you probably want to have a talk about acting and how porn isn't reality.

Jimmy, well, Jimmy saw a videogame character tied up and it made him feel good, so he starts looking for that online. He's about to explore the BDSM scene. He's going to need the "safe sane consensual" talk, otherwise his explorations might get him, or someone else, hurt. He'll need more of a talk than Timmy!

Harry loves hentai; he found some when looking for pictures of his favourite cartoon character. Harry is going to need a long talk about fantasy Vs reality, otherwise he's going to disappoint a lot of women! Wait a moment, most of the things he's looking at involve animals and women... Might be time to get some therapy!

In all three of these cases a different style and level of parental intervention was required. You watch your kids because they're kids, and kids are experts at getting themselves (and others) hurt. Parents need to watch their kids because it's their job to intervene, and to decide the method of intervention.

However, we've not gone over the case of Lizzy, a girl cursed with religious fundamentalist parents. When they find out she's more interested in girls than boys, she'll be subjected to inhumane treatment to "fix" her. So there is a grey area here - not all parents should be parents.