Bold emphasis is mine.
I know the above quote isn't actually your words so my comments are not directed to you specifically.
Mr. Painter talks about "muscle strength", and muscles flexing and relaxing. I would expect that the goal of this type of training is to keep the muscles from flexing, in order to train something deeper and more global, correct?
The muscles whose function is to move are the global muscles and the muscles whose function is to stabilize are the local muscles. You are strengthening the local/stabilizing muscles by relaxing the global/mobilizing muscles so that the global/mobilizing muscles are not doing the function of the local/stabilizing muscles.
"Global muscles are very important for movement of the limbs and trunk. Their job is to move the body. They generate a lot of force, move the body then relax.
The deep stabilizers:
* Attach directly into the lumbar spine at each level
* Turn on before you move to support the spine and pelvis
* Turn on and stay on as you move
* Work at a low intensity and stay on for long periods of time
* Work independently of the global movement muscles"
And what about the "feeling" created by movement without movement, through a relaxed body? What is that, exactly? Is it like the feeling of a sudden drop in an elevator (just as a crude example)? This isn't just supposed to be a trick of the imagination, is it? Something is supposed to actually happen that triggers a "feeling," that isn't an obvious muscular contraction.
You can not directly feel the local/stabilizer muscles contractions, like you can a global/mobilizer muscle.
When the local/stabilizer muscles are doing their job of stabilizing the body, the body is well balanced against the pull of gravity ( good posture) and the global/mobilizer muscles do less work ( not helping to stabilizing the body). My experience is a feeling of lightness and warmth inside the body. The stabilizer muscles at work generate heat that is an indirect indication of them working. Also since the mobilizers are actually doing less work they don't tire as easily or quickly.