Don't know if this is still the case, but it used to be possible to target one specific individual (yegg wrote http://www.gabrielweinberg.com/blog/2010/05/a-fb-ad-targeted... about it), and it was possible to cross reference this with other RTB venues (e.g., adnexus) - so that, while they didn't give out your details - if you were targeting someone specific, you'd actually get to see a significant part of their web traffic (everything that had ads through those RTB venues).

It all boils down to what you mean by "identify" - if you include "complete name, address, age, etc." - then, no, FB doesn't directly identify you. But if you mean "know whenever that same user does anything else anywhere", then - yes, they do let the advertisers identify you.