That county DA doesn't give a shit how rich you are. Being rich doesn't get you out of "poor people" crimes that revolve around physical evidence (as opposed to "rich people" crimes that revolve around knowledge/intent).
There's a great scene in "Michael Clayton" where a rich banker calls his lawyer because he hit a bicyclist in his car and fled the scene. The lawyer basically tells him: "I don't know what you think I can do for you, you're fucked." It's a realistic depiction of this situation: http://www.youtube.com/watch?v=J-ckEptxp3s.
The lawyer can give legal advice on what to say and not say, how best to approach the issue, what looks best when taking it to court. Maybe not get off scot-free, but minimise the punishment. Are there any options other than fronting up to court? Mediation? Medical costs? Perhaps filing your admission in a different jurisdiction might help (though I doubt it in the given case)?
Even just having someone who's calm, collected, and dispassionate speak at the trial can be an advantage.
In a criminal charge for something like battery, a lot of the usual legal maneuvering isn't available. There's no mediation, no settlements, no forum shopping jurisdictions, no expert witnesses. All you've got is a prosecutor who is trying to make an example out of you and police with evidence showing you did it. Ultimately, you're going to get the punishment the judge and the jury think you should get.
Now, that doesn't mean you're going to get the same punishment as the poor black guy, but that's not because it helps to be rich, but because it hurts to be poor or black. Juries don't give poor black guys the benefit of the doubt, they have trouble empathizing with people of a different race, their character witnesses don't come across as sympathetic, etc.
There's a great scene in "Michael Clayton" where a rich banker calls his lawyer because he hit a bicyclist in his car and fled the scene. The lawyer basically tells him: "I don't know what you think I can do for you, you're fucked." It's a realistic depiction of this situation: http://www.youtube.com/watch?v=J-ckEptxp3s.