My husband and I check our teenage daughter's e-mail from time to time. I also sometimes check her web posts, just as a precaution, although she is quite discerning and lets me know if she has any interactions she finds uncomfortable. We trust her intentions, but not always her judgment.
My husband will sometimes look over my shoulder at FR and say, "HuH?" which is a signal that he'd like me to pay more attention to real life :-). And I will talk to him about any exchanges that disturb me.
Could it be that this family is ok with what they do? I'm sure their website provokes alot of people to send them alot of evil stuff.