SOOOOOOOOO....
Hows them shoes taste? Did you take pictures? if you've not eaten them yet, do film it. it needs to fo on youtube!
Simple. Begins/TDK and even the impostor Keaton Batman and his foul murdering ways are just slices of the mythos. Batman is much bigger than just a single film, and a single version. or even a single universe. Hell, in the current comics, even he gets this now and has started to franchise.
Gordon is important to the Batman Mythos, almost as much as the Joker. For that Matter, the amount the Joker picks on Gordon directly should serve to to show this ( not just in TDK, but in ALL batman continuity). i'd take ANY realistic version of Gordon, so long as he looked SOMETHING like how he is depicted in the comics/animated series.
one final note , as i'm sure it'll be brought up.
batman doesn't kill. NEVER should kill, he always finds another way.
The closest he comes is refusing to save someone.
If you'd like to see a definitive characterful version of batman, may I suggest you go watch Batman under the red Hood?