L. A. Confidential: (how) does <PERSON> hear what's said outside the interview room?
At the end of L.A. Confidential, <PERSON> is in a (supposedly) sound-proof interview room, giving a statement to two detectives. He is observed by a group of others, including the chief of police and the DA, who sit outside the room behind a one-way mirror. They supposedly cannot be seen or heard by <PERSON> (a scene from inside the interview room shows only <PERSON>'s reflection on his side of the one-way mirror window).
After <PERSON> finishes his statement and the two detectives leave the room, the police chief and DA confer and we get the following dialogue:
DA: Who's to say what happened? Maybe [spoiler] died a hero?
[<PERSON> smirks]
Police chief: You wanna tell me what you're smiling about?
<PERSON>: A hero.
Detective 1 (outside interview room): How did he know what we were talking about?
Detective 2 (outside interview room): He couldn't have heard us.
Police chief: And?
<PERSON>: In this situation, you'll need more than one.
If you watch the film carefully, it goes to great lengths to show us that <PERSON> cannot hear the DA's line of dialogue:
* We clearly hear the door to the interview room close as the two detectives leave, well before the DA's "hero" line. 918
A subsequent shot from inside the room confirms that the door is closed.
* In the shot of the DA and the police chief having their "hero" conversation, the intercom button they need to press to be heard inside the interview room is in clear view in the foreground, and is not being pressed.
* The police chief's first line ("You wanna tell me...") is heard from within the interview room, but we clearly hear the intercom engaging before it and disengaging afterwards. For his "And?" line we're outside the interview room and actually see him press the intercom button. (By implication, if the intercom is not used they can't be heard.)
* And of course, the two detectives comment on it explicitly.
I've watched L.A. Confidential many times and this scene has always puzzled me. Does <PERSON> really know what's been said, and if so how? Or is it coincidence or a lucky guess? If so, why is it included: just to indicate <PERSON>'s sharp instincts, or for some other reason?
I wonder if there's a reference elsewhere in the film that I'm missing, or whether perhaps it's a sequence from the book that has transferred clumsily in the adaptation. (I haven't read the book.) 918