Thanks,
This was my theory and I was just looking for confirmation.
While not formally trained beyond my Pa's hunting skills and the U.S. Army Drill Sergeant's skills, I do know the fundamentals and can generally shoot sub MOA with my cheapo Rem 700P LTR, but it only has the factory H&S stock and no pistol grip so the thumb squeeze doesn't seem to factor into my hold as much as it can with pistol. I find I have to use a sling to pull/push and load up the bipod with that setup to get the best groups.