Because this DA had a very weak case. A face saving deal.
That's probably most of it. Plus, the DA would have to prove "doctor shopping" in trial, which would mean he'd have to prove intent. And, I would think the DA might have some difficulty getting testimony from doctors against Rush, and then he'd have to get a jury to find Rush guilty. Rush probably agreed to this deal because he didn't want his whole personal life smeared, either.