OP, where exactly are you seeing these "spine shots" that drop the animal on the spot? I presume you're talking about the neck, right?
On my first deer hunt I hit a deer full on in the chest (30-06, maybe 30 yards) and he went down like a sack of potatoes. I figured it was due to the shock of the physical impact.
Maybe that's the mechanism responsible.
I know my human anatomy and there's certainly nothing in the neck that "instantly" kills when damaged, although damage in the upper to middle spinal cord will certainly stop breathing (C3,4,5 keeps the diaphragm alive) and any damage to the spinal cord of the neck will instantly paralyze.
I'm speculating here, but maybe it's the hydrostatic shock to the spinal cord that causes the deer to drop (similar to knocking out someone if you hit them in the chin at just the right angle)