The following is taken from the Batman: The Animated Series Volume 1 DVD set.
Bruce Timm talks about how the show came to be, and if you look close at some of the episodes on the 4 disc set, there are references to Tiny Toon Adventures, which Timm, Tom Ruegger, and others were working on prior to Batman. They will tell you upfront that the audio track for the pilot was lost, and the familiar theme, composed by Danny Elfman, was inserted instead for the DVD release.
Basically, the dialogue tells us a lot of things we already knew.
At least now you know how they came up with the iconic open for the show, or at least part of it.