Willie seems to this quite a bit with his guitar work as well.What you're referring to is subtle but palpable. It requires masterful timing and feel. Playing around the beat, either just in front of it or just behind it, doesn't involve tempo changes at all. It's a matter of splitting hairs with notes. To do it well, you have to be off and on simultaneously, if that makes sense.
Willie Nelson does this with expert application in his vocal parts. He'll sing a tad in front of or behind the beat, then synchronize himself with it unerringly, all the while making the maneuver seem as natural as breathing, introducing no disruption to the music at all. Character abounds as a result.
Funk drummers employ this method quite a bit. It adds a rhythmic edge to the music. The sensation is similar to pulling yourself back right before you fall off a cliff, regaining your footing as though nothing amiss took place. The effect contributes a lot of spice.