Apparently NBC was going to edit Bush out of the tape in the story they were doing, but they got beat to the punch. 
They weren't beaten to the punch, they were the only ones with that material, they had a solid hold on the story, the timing of it, everything. For all we know, NBC says they were waiting until after the 2nd debate to release the story (perhaps to not weigh too heavily on the event), but even that is taking too much of a meddling stance on things.
The raw footage was leaked to the Washington Post, as in some dude there got an anonymous package in the mail. Perhaps the person who leaked it thought NBC was going to kill the story outright, and perhaps they would have, for whatever reasons. When people get bothered by 'the media', this shit is exactly why.