The key is, "Well bedded."
Quoting from Warren Page's book, The Accurate Rifle, he states the following.
"Bedding, the relationship between the metal parts and the stock-- is one of the two or three most critical elements in the precision balance we call accuracy."
I have stated on these threads many times that my rifles usually shoot better with pressure under the barrel, at the tip of the wood. This seems to be a controversial subject, so I will quote here from Warren Page's book again, regarding this subject.
He is describing stock making. "Then the barrel groove is cut out so that out at the fore-end tip enough wood is left so the forestock pushes up against the barrel with pretty fair pressure, enough to require significant effort to seperate barrel and forestock tip. The theory is that this pressure will cut the peaks and hollows off the vibrations of a relatively slender barrel and a relatively violent cartridge."
Among the many accomplishments of Warren Page, was his winning of the annual US National Match bench rest shooting competitions nine times.
Back to the original question, I have many times taken the stock off a scope sighted rifle, that had pressure under the barrel at the stock tip, and when the stock was replaced there was no discernable change in poi.