I think Finger should be credited as the creator of Batman, period.
For what it's worth--and I realize it's not worth much, with only scant circumstantial evidence--I actually get the impression that "someone" used Finger to slip the Batman ideas to Kane with sufficient plausible deniability in case of a lawsuit.
Dial B gives a fairly good overview of Kane's part in things, including the reconstructed "Bird Man" and from what it "may" have been derived:
http://www.dialbforblog.com/archives/389/He then goes into the transformation from bird to bat, but it's a melange of weird, overly specific, and contradictory details. Webster's Dictionary, for example? The ears becoming a cowll? The gloves?
Of Finger, he says, "Finger was insecure. He was not good at standing up for himself, he was a Signaturesperfectionist who had trouble meeting deadlines, and was sometimes plagued by writer’s block. He would later develop drinking problems." Yet he remembers this clear as day, but didn't want a lick of credit for it. Hm...
Meanwhile, not far away, Norman Daniels had created (earlier that year, but as-yet unpublished) a character with almost exactly the same look Finger describes (minus the ears), the Black Bat, for Thrilling Publications. Heck of a coincidence, there.
http://en.wikipedia.org/wiki/The_Black_BatIt was so much of a coincidence, that both Nedor and National threatened to sue over copyright infringement. Neither case went to court, though. Why? Because Whitney Ellsworth--who had just recently left National for some time off in California and had worked for Ned Pines a couple year prior--wandered out to broker some kind of deal which seems to have boiled down to "nobody sues."
Every bit of that strikes me as really, really suspicious. Maybe I'm too conspiracy-minded, but it all reads to me as if Ellsworth assumed the Black Bat (a good character idea) was forgotten or dropped at Nedor. They bring in Kane to supply the strip, figuring if Pines were to sue, the artist who, frankly, traces his only decent action shots is more than expendable. But Kane doesn't really pay attention, or wants to do his own thing, so he puts together "Bird-Man." Finger then gets recruited to push Kane back on track, or to "improve" Bird-Man by adapting features of the presumed-discarded Black Bat. He does it, but tries to keep out of the spotlight, since he'd rather not be associated with it. And when Batman turns out to be too much of a success to lose, then Ellsworth takes the bullet in private and leaves town for a year or two. (And later comes BACK to not just National, but Nedor, working on both Batman and the Black Bat in the '40s.)
Mind you, I don't want to malign anybody or imply that there's hard evidence to back my theory up, but this seems like a closer fit to what we know than all the hodge-podge elements that Kane and Finger cited over the years, in the same way that Superman's resemblance to Philip Wylie's "Gladiator" novel could never be discounted even as Siegel claimed he had never heard of it.