Parents could look at this as an early lesson in internet safety and as a way to communicate with their children and build trust early on. This will take work and careful monitoring since you should set your child's security settings to high protection and learn how to use facebook yourself to best protect them.
If you are teaching your children not to talk with strangers, perhaps you can parlay this into the online world as well such as "remember what mommy says about strangers" Don't talk to strangers on facebook either."
"No information from children under age 13. If you are under age 13, please do not attempt to register for Facebook or provide any personal information about yourself to us. If we learn that we have collected personal information from a child under age 13, we will delete that information as quickly as possible. If you believe that we might have any information from a child under age 13, please contact us through this help page."
"Parental participation. We strongly recommend that minors 13 years of age or older ask their parents for permission before sending any information about themselves to anyone over the Internet and we encourage parents to teach their children about safe internet use practices. Materials to help parents talk to their children about safe internet use can be found on this help page."