Batman is open to many interpretations. However, going back to Bob Kane and Bill Finger, continuing through Adam West, Denny O'Neill and Steve Englehart and up to Frank Miller and others, it was always "Bruce Wayne in a mask." Bruce Wayne just happens to be obsessed with avenging his parents' murder by warring upon criminals while wearing a mask.
Frank Miller was the one who pointed out and defined the functional distinctions between the two personalities. If he's to be believed, that's the reason why so many writers were angry with him after he wrote DKR.
And I can't prove it, but I'd like to think that Bill Finger thought the same way. I'm pretty sure he was feeding Bob Kane lines when Kane clarified that character's mission would have been cut short if he had known who the killer was from the get go.
Above all else, what I'm saying is that Nolan and Goyer were both aware of exactly which defining moments they needed to properly change the player from Batman to Bruce Wayne: instead of having a faceless killer that Bruce Wayne and Batman associated with all of crime, they instead had Joe Chill. So even if there are different interpretations, they in particular were still operating off Frank Miller's observation.
