Bruce's Arrogance?

I've heard about Batman #37 and I'm kind of surprised no one is talking about the implications.

SPOILERS AHEAD

I've always thought that on some level Joker knew who Batman was. In DITF it's heavily hinted, which makes sense as Batman calls his murdered Robin by name and Joker in later stories refers to Shelia Haywood as Jason's mother. Something he couldn't have known unless he knew Robins' ID. Joker just looks Bruce Wayne in the eye and laughs without comment. Why would he tell anyone when it's funnier--to him--if it's a private joke? Revealing it to the world ends the game they play.

Naturally things differ some in the new 52 and in this version he visits Joker as Bruce Wayne and gets no visible reaction. He assumes that because he knows Joker so well he knows Batmans' ID is safe because Joker wouldn't want to know. Yet all his attacks on the family were personal especially Jason's fight against him. Now we have Joker calling Batman by his name. Will Bruce tell the others and own up on his failure to protect them? The confirmation is something they'd deserve to know.