Why would he run towards Wilson, and what evidence do we have that he did? Last time I checked, all of the eyewitness testimony said that Wilson had been chasing and shooting at Brown until Brown stopped, turned around, and put his hands in the air, and Wilson advanced on him and shot him, and continued to pump shots into him until he was on the ground.
Supposing a consistent trail of blood drops are found behind the body, it's possible that Brown could have run away, stopped, put his hands into the air. Then, in that moment, Officer Wilson decides to murder the young man. Wilson starts shooting so, in self-defense, Brown runs toward Wilson.
The unofficial police officer scenario is that Wilson fired, perhaps not intending to strike Brown. Brown stops, turns around, maybe even holds his hands up in the air. Then Brown decides, "You're not gonna shoot me," and "bum-rushes" Wilson.
Between the two, the second scenario sounds more plausible. If a still person takes gunfire, I'd expect the victim to twist, turn, duck, and or run away. (Away, not toward). That's not decision but an instinct. It's much more difficult to twist, turn, duck and dodge after one has gathered forward momentum.
Now, why on earth would Brown decide to rush a cop? Is that something that sounds ridiculous or stupid? As mentioned already, stealing cheap cigars fits the bill for stupid. It also seems impulsive. Just walk into a store that likely has video cameras, no mask, openly grab some cigars, and make a bigger scene with a show of force?
Between the two, we already know Brown's the one who has behaved stupidly and unlawfully. While it's possible Wilson's behavior is far more criminal, I think it's less likely.
