I think the best advice for parents is to assume the internet is an unsafe place for their children to be socialising.
There are plenty of examples where children have been stalked by predators.
A recent article on Mashable says an investigation found 300 registered sex offenders from Kansas alone were registered on MySpace.
That was only the ones dumb enough to use their real names.
I was in a local court recently when the magistrate imposed conditions on a man bailed for a later appearance that he not visit internet chat sites.
I suspect the men being monitored are sadly just the tip of an ugly iceberg. With a 13-year-old daughter myself I don’t want her communicating online with anybody she hasn’t already met.