Personally, I think trust does play an important roll in this sort of thing. My daughter and I are lucky in that the children trust us enough, that they are quite happy to, have us as friends on they're fb account.
Everyone wants to keep they're children safe, and one of the best ways is to make sure that the children can talk openly about any subject, and are quite happy to ask for advise regarding anything that they come across. They are also willing to take advice, because they know it is becaue they're parents love them, and are concerned for they're safety. We can never keep our children 100% safe, but we can give them the tools they need to give them a head start.
Also, how someone deals with this sort of thing is also something for the individual parent. We are all different, have different experiences, views etc. It is not for me to tell a parent that he or she is wrong. Go with your instincts and what you feel, is right. Thats the best advice. And good luck. Bringing children up is a hard job for anyone.