Parental controls can be introduced to stop access to certain sites or to contain access to pre-selected sites. The problem with the situation you mentioned is that they are using the net to avail of free communication software (MSN messenger in this case) and thus can still come into contact with the "weird people she might come across" through this system.
A relatively cheap solution to supervision can be to hook up the PC to your TV (just a few simple wires to do this). This can allow you or your OH to flick to the AV channel and see exactly what is happening on the PC. It still has the "looking over the shoulder" problem, but no software solution (at least that I am aware of) will totally cut out the chance of random people contacting someone through msn etc.
Discussing concerns with your daughter you can explain the problems (or potential problems as you see them) and ask her to ensure she only chats with her known friends, if this may relieve some of your worries. As much as you do trust your child, everyone does, the knowledge that mum or dad could possibly be watching what's happening may give an extra piece of mind to yourselves.
You'll have to question the issues with Privacy Vs. Security from your own point of view, it's not something anyone else can decide for you.