Here is some more, straight from Geoff's site;
Whenever the shoulder joint (armpit) opens or closes, there is independent arm action. (There is also independent forearm action when the elbow joint alters in the stroke.) This agrees more or less with your second option above:
"Solid shoulder structure will lock the scapulae to the thorax, and the upper torso will have to be rotated to execute a putting stroke."
Your terminology is a bit different than what I would use. I would not say "solid" or "lock", as this is not how the shoulder and torso interact in movement. The gut and lower back muscles basically move the upper torso as a unit, and this simply carries the shoulders with the motion. The upper torso motion flexes the lower spine more than it does the thoracic spine, so the upper torso more or less stays as a unit in the motion. The most motion occurs in the lower back. I would also not say "rotate", as this is not quite what the lower torso is doing. The lower torso is flexing side to side. This carries the lead shoulder in plane headed beneath the pivot at the base of the neck, and then reciprocates the other way. The actual extent of movement of the lead shoulder itself is not that great -- perhaps 3-5 inches total in space. The way the pivot stays in place is complicated, but involves some combination of the hips shifting sideways or the upper torso causing a stretch away from the hips on one side. It all concentrates low in the abdomen, near the hips. It is quite possible to hold the neck and head still in place as the upper torso flexes down and back and then up and forward.
If the stroke motion is more of a gating action, this alleviates the stretching a bit, but brings its own problems into play.
With either stroke motion, the pivot ends up being the key -- either keeping it still in place so the stroke re-squares the putter in the middle of the stroke before impact, or by the pivot moving in a carefully symmetrical pattern back and forward.