I have just seen the back cover for The Dark Knight Returns blu-ray which includes this featurette.
Now hear me out on this as i have theory why Warner Bros have included this.
With the recent release of Bill the boy wonder book, documenting how much work Bill Finger did in helping create Batman and the press it's got, i think that Warner Bros have panicked as such and they want to really push that it was Bob Kane and only Bob Kane who did the work. They know that this film will be seen by comic fans everywhere and also the media as its one of the biggest batman stories ever written. So what better way than to include this story about Bob Kane.
It also may seem that there isn't a problem in getting Bill Finger's name on the creating credits Batman, Warner just won't do it.
Bill Finger's ex wife Lyn Simmons contacted Warner Bros about getting Bill's name on the credits for Batman89, after her son steven had done the same. Steven sent a letter to his mom saying that Warner Bros had agreed. Lyn then got a letter from Warner Bros. starting she had to waiver all rights which she did.
It then seems Warner Bros back tracked and called her to say his name wouldn't be included.
The letters can be seen here.