After watching the excellent slo-mo video posted earlier in the thread I saw that, despite a mechanical release, there was still sideways oscillation in the string. Sideways oscillation presumably throws the nock left and right whilst the rest contact stays constant(ish). It seemed therefore that the purpose of paper tuning is to align the rest, string and target in a straight line at point of nock separation. Thus producing bullet holes.
Torque in the grip would most likely cause or exacerbate this sideways oscillation. Therefore consistent torque in the grip could cause reliable, repeatable oscillation. Meaning it would be possible to paper tune to compensate for torque. Not that you'd ideally want to but it's a compromise between the ideal robot precise grip and a squishy human.
In walk back tuning you move the sight at close range and the rest at long range. So if the arrows started landing right at long range with a better grip. I could move the rest left, away from the riser. I have doubts that this part of my logic chain is true though. As you say, torque also moves the sight, causing aiming problems. I suspect that after a grip change you should paper tune again.
EDIT - the whole theory is complete rubbish. My brain must be thinking these things over while I'm asleep. Anyway, I realised that running my theory backwards I should be able to look at rest vs string position and determine what the original paper tear was. My rest is a long way to the right. If string oscillation is the cause then the string must be to the right as well. Meaning that, if my rest was central, I should have had a tail RIGHT tear instead of tail left.