Picture a snake swallowing and then passing a golf ball. That's kinda like what happens when a projectile travels down the barrel. The thicker the barrel, the less vibration/distortion, so heavy bull barrels are inherently more accurate.
Without a free floating barrel, the bottom of the barrel won't vibrate in the same manner as the top, since the stock will interfere. It's this disparity between the movement of the topside of the barrel vs the bottom that affects accuracy, along with several other variables. If the stock was bedded, but went all the way around the barrel, it wouldn't be as much of an issue, as its affect would be distributed uniformly around the circumference of the barrel.