Schubert, great question. The answer is, not surprisingly I’m sure, "all of the above". That level of musical intuition is a combination of innate ability ("great ears") and musical maturity gained by learning the importance of knowing when to support a musical colleague and when, and how much, to make it about one’s ego; all for the good of the music. Aside from whatever level of innate ability a musician was blessed with (or not) those are things that can be worked on and developed. While that work is a kind of "shedding" it mostly requires playing with others. To the point that I think you implied re "shed time": a musician can be blessed with the highest level of innate musical intuition possible, but ultimately he has to be in total control of the physical mechanism of playing or singing (achieved by putting in a lot of "shed time") otherwise the body cannot translate the musical messages that the brain/heart sends in a way that is physically controlled enough to allow the kind of musical cohesion that you are hearing in that clip.
To your second question: if one considers what the very best examples there have been throughout the history of the music I would rate that a solid 8. Acknowledging a certain amount of inevitable subjectivity, for me, Miles’ classic quintet from the 60’s with Wayne Shorter, Herbie Hancock, Ron Carter and Tony Williams set the standard for that kind of ensemble musical intuition as did the Bill Evans trio with Scott Lafaro and Paul Motian.
To your second question: if one considers what the very best examples there have been throughout the history of the music I would rate that a solid 8. Acknowledging a certain amount of inevitable subjectivity, for me, Miles’ classic quintet from the 60’s with Wayne Shorter, Herbie Hancock, Ron Carter and Tony Williams set the standard for that kind of ensemble musical intuition as did the Bill Evans trio with Scott Lafaro and Paul Motian.