> If you have ever signed into FB from home, they know that machine / ip / whatever fingerprint is you. Even after you sign out, its still out.

Even if you signed out, they probably still have a cookie tracking who you are, and when your browser fetches that Like button, it will still send that cookie to the Facebook server. It'd be interesting on a shared computer where 2 people (e.g. a brother and sister) log in to FB alternatively, but I guess they can still distinguish who is who (e.g. person visits gaming forum, person visits this product page, person visits page with pics of a female supermodel: presumably it's the brother visiting all 3 sites. It's a bit sexist but that's what the algorithm would guess.)