Officer Wilson pulls up alongside the dimwit duo and tells them to get their a...s back on the sidewalk in a terse tone of voice. Johnson, who is little more with it than Brown, takes off. The 6'4, 300 lb Brown who had just showed a 5'5 120 lb storekeeper who was the tough guy, decides he doesn't have to take any crap from some white motherf..... cop. So he continues walking down the middle of the street.
Wilson stops the car and starts to get out. Before he gets all the way out of the car Brown charges at Wilson wildly swinging his fists knocking Wilson back into the car. He jumps on Wilson and reaches for Wilson's gun. Wilson gets it out first and tries to shoot an enraged Brown who Wilson thinks has gone crazy. Wilson gets a few shots off hitting Brown in the hand and a non-vital part of Brown's body which fails to calm Brown down.
Brown retreats ten or so feet from the car, then seeing the bruised and (what he thinks is) disoriented Officer Wilson, charges meaning to get the gun and finish off the white, motherf..... pig. Wilson, however, is still conscious, and manages to fire six or more rounds hitting the charging Brown six times one shot ripping into Brown's skull killing him. One less ghetto thug in America. That's the way I see it.
The scenario you describe sounds exactly right.
I bet that is almost exactly what happened. Far, far too many black youth only understand violence and racism.