If the bits going through your router were the only way Facebook gathered data about you, that would make sense. But it's only one way. You don't even need to have a Facebook account to have a Facebook profile.
So how is Facebook filling up my profile with no input data? They might create a profile based on data my friends publish, but they won't be able to connect it with my IP or my identity.
I found none, that's why I'm asking. There is technologically no way to connect me (my browser/phone that sends no information to FB) and my "profile" made up by a few photos of me that my friends have uploaded.