Henny what hes saying is that moving the shoulders does NOT mean you are pivoting. You can have a stroke with no pivot at all but you could still move the shoulders.
The shoulders are part of the power package ie they form the second side of the triangle (6-A-1).
This is why the page (7-13) is titled dual agent as the shoulders are part of the power package (Zone #2 (9-2)) and part of the pivot (Zone #1 (9-1)).
Take a look at pictures 10-12-C#1, 10-12-C#2 this is a zero pivot and look how much Diane has turned her shoulders.!
Acquired motion (12-5-2) "...zero to minimal pivot...and any needed shoulder turn"
Sounds to me like youre talking about using a shoulder only stroke for your putting as is common on tour. Take a look at this thread for more discussion.
Your post confirms how I read it. I do putt with a tour-style action, but I definitely feel lag. The linked thread is out of my depth, so I'm going back to my hole on this one.