He's not on probation. Probation is a sentence subsequent to conviction. Rush has not been indicted.
He's in a diversion program; if he complies with the conditions of the deal, the charges will be dropped without ever going to court and he will have no record.
There was some howling at the time about Rush getting a "sweetheart deal." I checked with my dad, who's worked in the Georgia Department of Corrections for about 36 years, and he told me these diversion arrangements are pretty standard for first-time, non-violent offenders who aren't at high risk to re-offend. It's not in anyone's interest to put them into the system.
Then Rush wasted a lot of dough on that fancy attorney.
Rush could have gotten the same deal with a public defender, since as you stated, he got the standard deal for first-time offenders.