I believe you have that backwards.
No, not really. The prosecutor has been through months of bogus investigation, and spent lots of money on it. At this point he could go ahead and file charges, and lose, and bring more scorn down on himself. With this gambit he basically saves face and can say "hey, it didn't cost the taxpayer anything. Which is better than losing in a jury trial, which is where this dog was headed.
As Rush's attorney points out he was going to do what he's required to anyway (one doctor, no drugs) so there is no downside, other than the $30,000. Lets face it $30,000 to rush is like $300 to you or me (well I don't know you, so I'm assuming your not worth $500 Million like Rush).
I was charged with a completely bogus traffic offense that was a misdemeanor last year. Eventually it was dismissed with prejudice (DA can not refile) but I had to pay $250 bucks in court costs. Conveniently, there was an ATM machine in the courthouse.
As going to court is very expensive (missing work, etc) anyone who has the opportunity to have charges dropped for a small amount of cash will do so. It would have cost me more to have my attorney come back to court one more time, only a trial probably would have taken several more times, not one.
They got you by the b*lls in these situations, and they know it. Having been through this experience I'm a lot less of a supporter of LEOs and DAs than previously. Sure some risk their asses and deal with really bad people. Others make big mistakes, won't admit them, and shakedown citizens with scams.
This is a deal that Rush and Roy Black brought to the DA; it's their deal and their face saving.