Given that I regularly see my Facebook account name and photo on third party websites, without giving them any permission to see those, I find it hard to believe that Facebook cares about this…
I agree with theGimp. From my experience they do seem to care about this. I actually still carry the debt card they sent me in my wallet (http://imgur.com/TuVKm5k). Facebook also seems to be the most generous in terms of giving out a reward. I ended up submitting a few more issues after this and always got something reasonable (usually 1k to 1.5k).