You can view browser headers and see this for yourself, if you're curious. In Chrome, go to the Developer Tools -> Network Tab, refresh a page with the "like" b

You can view browser headers and see this for yourself, if you're curious. In Chrome, go to the Developer Tools -> Network Tab, refresh a page with the "like" button, look for "like.php" and all the corresponding resources loaded by it, and look at the "headers" tab for each. You can see what data is being sent to Facebook and draw your own conclusions about how anonymous it makes you.