I asked the manager of the machine shop where I worked about this. He said to bring in a barrel (no action or any other part of the rifle) and he would show me something. So I brought in a 30 caliber Obermeyer cut-rifled blank heavy match barrel and a factory Win. 70 .30-06 hammer forged sporter barrel.
Ater work hours, he laid the Winchester factory barrel ends on surface plates atop a granite gauging table. Each end of the barrel was on a very smooth, perfectly flat surface. The barrel slowly rolled until one side was down. Removing then replacing the barrel with that down part up to one side or another ended up with the same point down on the surface plates. He said the heavy side of the barrel made it move down from gravity. That barrel's bore was enough off center in its profile that one side had a weight advantage.
Then he did the same thing with the Obermeyer barrel. It barely spun after laying it on the surface plates at each end. That master machinist said it was very well made with the bore well centered on the barrel's profile and there wasn't enough mass on its heavy side to overcome the surface friction between the barrel and the surface plate to let gravity have its way and pull its heavy side down.
He also said there were "friction free" bearings that could be mounted such with centers in them that would show the same thing on any thing. Its heavy side would always move down. Such would be better for rifle barrels as their surfaces tension due to minute roughnes at their edges would have enough friction that exact unbalance amounts may not be visible.