I would say that internet became a public place, and just like a public place there are "safe" zones and not so safe. It's no different then letting your kids run around town by themselves. If you prepared them for the world out there, then they'll be fine for the most part; you know, the old "don't talk to strangers" routine, "look both ways before crossing the street". But on the other hand, it you're an ignorant person, busy with your carrier and hope that school or some other outside forces will fill the gap in preparing your child for the realities of the outside world, then you're asking for trouble and most likely the kid will get hurt or at the least get very confused. Oh and by the way, there is no such thing as "safe", it's an illusion, a construct created by people that lost touch with reality. The so called "safety" is very subjective, I can walk downtown most metropolis at 3am and I feel "safe", on the other hand, my paranoid friend, who pays WAY too much attention to sensationalist news, thinks that everyone is out to rape him. But in reality we're both just as "safe".
©Of course, it's just my opinion and I could be wrong :)