The isolation of the parts that Gadd demonstrated was the breakthrough for me.
Listening to the audio rather scared me, as would seeing a transcription. But I admit that's my fault, not the fault of the educators.
I originally learned the correct sticking/footwork from a transcription, but like Chris I tend to learn a lot from watching things done. Seeing them done provides an insight into some of the subtleties of the part that can't be expressed as well in notation. Things like small dynamic changes through the bar, internal dynamics (sound levels), the emotional mood, and even sometimes the body language of the player reveal so much about the part.
For instance, you pointed out the volume Steve played at. That's something that can be expressed by dynamic markings to some degree, but those are often relative. Really important elements like the articulation of the two BD 16th notes on the "a" of 2 and on 3 aren't usually notated. Those are played bi-BOOM. Play them as BOOM-BOOM and the pattern loses its swing. In this video we don't get to see his feet, but elsewhere we can see the technique he uses on the foot pedal to get that "bi-Boom" articulation. Those small details are the real nitty-gritty of Gadd's style.
Watch how his body sways into 3 - perfectly expressing the rise and fall/tension and release of the groove. It's like we breathe in on 4...1...2...and out on 3. Rest and breathe in again. Beautiful.
Anyway, here's another video of Gadd recently added to Youtube. Part way through there is another example of Gadd playing open-handed linear parts and generating a killer funk groove.
http://www.youtube.com/v/jSssS67uXOQYoutube can be a really great thing.