Wait a second, by ALL accounts this is what happened. By both Dorian Johnson's AND the police account, one shot was fired while Brown was at the SUV window. Why is it hard to imagine that one of those shots hit him in his arm? At that point, Brown fled. Darren Wilson exited his car and fired six more shots. I believe one of those shots also hit his arm. Brown turned around (witnesses claim with his hands up), said "don't shoot", and two seconds later, Darren Wilson shot him four more times, this time more deliberately, judging by the even cadence of the shots.
By the way, this part of the story can be reconciled with Wilson's version. If Brown said "don't shoot me", it's possible Wilson heard that as taunting or simply heard something different. "Don't shoot me" sounds enough like "You won't shoot me" for there to be an honest mistake. But whatever Brown said, he didn't have time to "bumrush" anyone, since the third set of shots started almost immediately.