Adrenaline alone can keep a person going for quite a few seconds longer than most people can believe, add possible narcotics to the mix (unknown, but possible) and a big guy like that can keep coming for quite some time even after getting hit multiple times.
My best friends father served in the marines during WWII, he island hopped and fought on many of the biggest battles there were, Okinawa etc. When he and I talked before his death my friend was serving in the first gulf war, 1Lt Army and we were fishing together waiting for news of the invasion to happen.
He told me a story that I have never forgotten, about being in a ditch with his .45 while a Japanese soldier was doing a bayonet charge at him. He emptied his .45 into the guy and he still had to jump to the side and run to avoid getting ran through. He told me the sheer determination on that mans face to kill him haunted him still to that day, over 45 years later.
A huge guy like this with his brain in attack mode, possibly hyped up but even without anything but adrenaline I can easily believe needing a head shot to bring him down after getting “stung” a few times in the arms.
What would have happened if Brown and his accomplice had gotten hold of the gun at the car? Or if Brown had reached the officer after running toward him?