PSN automatically "roots" your Facebook, no permission granted.
I'm being pedantic, but "roots your Facebook" is a massive misuse of the word root.I doubt Sony has the ability to do anything it wants with your account (It can't change your password, it can't revoke permissions of another app) so they haven't gained "root access" to your account.I also doubt that Sony is hacking or getting this access through illicit means. Sony doesn't "root" your account through some sort of exploit, Facebook has most likely given them that access. (As a few others have mentioned)You're right that this is disturbing. Poking holes into the security model in other to make the user experience more convenient is something companies do depressingly often. Here's an example that surprised me recently, if you activate your android phone by signing into a google account it ignores two-factor authentication and only asks for your password.[edit, removed a patronizing paragraph]