Everything you do on Facebook stays on Facebook regardless of your privacy settings, and deleting your account is impossible. Even if you delete your account, all your information stays on Facebook and can be recovered at any time.
The group accuses Facbook of selling information to the government, which Facebook denies. According to The Washington Post, Anonymous invites others to join the operation:
If you are a willing hacktivist or a guy who just wants to protect the freedom of information then join the cause and kill facebook for the sake of your own privacy.
ITProPortal says security experts doubt the authenticity of the video, saying that if it was authentic, there likely would have been some sort of talk about it on the social networking accounts of the notorious hacking group.