You do not need to be an active Facebook user, but you need a Facebook account to use FantasyBrain. You can simply sign up to Facebook and set your account to private. Think of it as your one-password solution that works on many sites across the web.
Simply follow the instructions to sign up to Facebook, after clicking the 'Login with Facebook' button. Once the account is created, click on the drop-down arrow in the top right corner, and choose Privacy Settings. Then click Custom, and in the pop-up dialog, select 'Only Me' from the drop-down box. Done! Easy ;)