I think children lying to get on these websites is one thing, they do so presumably to keep up with their friends who are on the same sites. But parents that allow their children to lie in order for them to get on these sites is something else altogether.
I also think that many parents are naive as to what children do and don't do on the internet, because although we can have parental controls at home, we have no control over what our children do online when they're elsewhere, at other friends' houses, the library, in an internet cafe ... and children are a lot more internet savvy than we give them credit for.
Also most children over the age of eleven have mobile phones, and many of these have internet access, and again parents would have little control over that, and it's easy enough to delete what you've been doing/who you've been talking to on facebook via your mobile phone without parents knowing.
I don't know what the answer is tbh, I think it's a worry that children have far earlier access to things that we never did, things which can compromise their safety, because as much as we tell kids not to give out info, most will at some time.