Naji,Matt, The problem is the natural pivot point requires the butt to be angled (left or right of cb center) in such a way to be effective, a player could mistakenly shift the butt hand left or right more than needed which will certainly changes the "natural pivot" point location, especially if his but hand position has to move all the way back due to CB at center of table! or say you have balls in the way, or feel very good with shorter bridge than long one!
You must not fully understand the back-hand pivot.
The pivot point is fixed by where the bridge is placed on the table.
The back hand moves the amount necessary to pivot the cue to apply the desired amount of english.
The pivot point (the bridge) does not move during the back-hand pivot. It is stationary.
FYI, illustrations can be found in the following article:
"Squirt - Part IV: BHE, FHE, and pivot-length calibration" (BD, November, 2007)
and demonstrations can be found in the following video:
NV B.71 - Cue natural pivot length and back-hand english (BHE), from VEPS II
I hope that helps,
Dave