YABU. Yes there are risks - but these are just online versions of what is happening anyway in the RL. Being on FB doesnt make them happen, just gives them a channel.
Yes, teenagers write rude things on their pages - and at times I have been shocked at the sexual content of what gets written by both boys and girls on my DS' page. But it is how they talk - it's just we don't normally hear it - and it's worse to see it written down.
Our kids live in a world where there is how they connect and communicate - stopping them using online tools is like our parents stopping us using the telephone. And you could genuinely be damaging your daughter's friendships if she isn't able to be part of the crowd, talk about the latest jokes, games and applications etc. At my DS' school, teachers use FB to manage sports teams, communicate about trips etc.
Rather than blocking access to technology, I believe we as parents need to learn how to use it and understand it for ourselves, and then to teach our kids to use it safely, postively and well. That means teaching them to think about privacy settings, to think about their reputations and how they present themselves online, making them aware that anything that goes up online is there forever and for everyone to see. Of course there are risks, but just as we teach them to cross the road safely (and then secretly worry every time we know they are doing it), so we have to teach them to use technology safely.