Joey also uses Neumann km184 Overhead mics which are top of the line and have some of the clearest and most accurate sounds. (but when you get into the really high end stuff, most OH mics are)
He also uses tube condensers as room mics which can help with cymbals in that "cleaness" along with helping with nice drum room sounds.
some of his pres are also top of the line (API, RME, ect)
So once you have the nice gear it should really help with getting nice sounding overheads. shitty Shure knock-off mics going into an mbox can get the job done but surely wont sound as clean as the natural sound.
and if he is doing live drums and the drummer is awesome I dont know why he would try to smash the room sounds out of the OHs (I know he used to but with recent mixes it doesnt sound like that at all, example being the new The Color Morale CD)
So now that we have covered the nice gear that most of us cant afford (184s and the 3124+ alone are over 5k new, amirite?)
The next best typical answer would be, the years and years of practice, hard work, different mic placements in your room, trial & error, and training your ear over time to get the sound you have always desired.
and Im sure he blends in on the miss hits with the samples he pulled from the kit.