People who shoot unaltered factory commercial actions with either original factory or aftermarket barrels typically experience point of bullet impact changing as the barrel heats up regardless of barrel stiffness. The more stiff the barrel is, the less that point of bullet impact changes.
People who shoot factory commercial or aftermarket custom actions with squared up receiver faces and aftermarket barrels properly fit typically experience no point of bullet impact changing as the barrel heats up. Doesn't matter how stiff the barrel is.
People have been shooting .308 Win. chambered 30" long "pencil thin" skinny barrels in the 4 to 5 pound range in properly trued actions for long range competition since the late 1950's. A typical barrel profile is Kreiger's #16 light Palma barrel listed in:
http://www.kriegerbarrels.com/Contours-c1246-wp3382.htm
My first Palma rifle's heavy barrel contour was the same as Kreiger's #10, its second light weight barrel was the same as the #16. Both shot equally accurate at long range and never walked shot impact as a 25 to 30 shot string was fired in half as many minutes starting with a cold barrel.
Every unaltered commercial Winchester 70 or Remington 40X centerfire match rifle I've shot, all with heavy bull barrels, walked their shot impact as they heated up. Didn't matter if they were .30-06, .308 Win, 28 or 30 caliber magnums. Epoxy bedding their receivers and totally free floating their barrels didn't help at all. Putting a pressure pad under the barrel at their stock's fore end tip made all of them shoot worse.
Unless one's shot such a properly built rifle well enough to observe point of bullet impact never changing as the barrel heats up, I believe they think and claim all rifles do that. They'll never observe the rifle and its barrel's accuracy does not change as the barrel heats up. The range of barrel temperature change isn't enough to cause a significant difference in how rigid or stiff it is.
But all of this will be difficult for some folks to grasp.