Do you think having a secret facebook account is safe?

My niece has made a secret facebook account. She doesn’t have many friends, but then again it is an account. She has trusted me that I won’t tell her parents, my sister and brother-in-law. The right answer, would be to tell her parents, but then again, this could lead to much bigger issues too. Her wall posts, her pictures, her unknown friend requests. Everything she has on facebook, is being exposed to the internet even more. Also, what if she doesn’t have updates? What is she doesn’t have any pictures that she’s been tagged in? What is she doesn’t have a profile picture? What now!??!Now, of course, tell her parents! They can help, however can they prevent this from happening again? Can they help keep her safer?
Ok, she is turning 13 this April. I want to keep her safe, but her parents have no awareness of this account, let alone Facebook. Her parents don’t have facebook accounts, one could say that they are “technically challenged”. They don’t know the Facebook privacy policy. They have heard of Facebook, but they just don’t know! I would tell them, but they are unaware of these dangers. Of course, they know that the internet has some insecure sites, bad viruses, and hackers/stalkers, but they don’t know a thing about facebook! What next??