In the world of professional swimming, there is something called an APM, or Assisted Power Machine. This machine uses wires to pull a swimmer through the water at speeds faster than they can normally go, giving them an experience of swimming at faster than they would normally be able to.
Contrast this with the old way of doing things, in which they used to attach wires that pulled in the opposite direction to provide resistance (they may still use these, for all I know).
Fundamentally,the difference lies in giving the athlete an experience of enhanced or impaired performance as part of their training. The theory behind the former (enhancing)method is that once someone feels what it's like to do something, one they experience it first hand, they'll be able to match that level of performance unassisted all the sooner.
The same thing can be said for shakuhachi practice. It comes from practicing with a highly qualified teacher. By playing along with someone who is truly a professional,the student experiences first-hand what it must be like to play at that level.
The quality of sound and technique is imprinted on their brain in a way that is not nearly matched by merely listening to someone else play, either live or on CD.Playing together gives the student an experience of playing at a higher level that nothing else can match. It's as if they are being pulled through the water on wires toward a heightened level of skill.