[runner]

Is that information private or the website owner can access it?

I mean, instead the website ask for email and username, it will ask authorization to import information from facebook... The website owner can find facebook account if he want, friends and all that... or that is private?

[Nachfolger]

Facebook should show you what information you're providing to the website via SSO--But yes, I'm pretty positive that your profile would be standard information given to the website. As a rule of thumb, SSO is never going to be anonymous.