Totally free floating rim and center fire barrels almost full receiver contact have shot best in shooting disciplines since the early 1930's. The only thing barrels should touch for best accuracy is the front sight receiver, cartridge and bullet. Maybe a slight touch of the bolt where it closes on the barrel. Best quality barrels shot better when folks stopped mounting those old long, externally adjusted scopes on barrels and started using shorter, internally adjusted scopes mounted only on the receiver.
Competitive shooters winning matches and setting records know this way beyond any doubt. They shoot enough shots per session with good gear and ammo the right way to see the advantages.
Others have all sorts of opinions about what should and/or should not be bedded based on a whole lot of things.
Regarding Slamfire's comments:
On older hunting rifles the barrels are closely inletted into the stock and on older M70's there are barrel bands. It is apparent that "back in the day" authorities of the era thought fixing the barrel in place was the way to go.
I wonder if it was due to the awful bullets that were in use back then. Maybe they were playing with bedding and could not distinguish between the effects of their bedding and random grouping.
Winchester not only had a screw up through the fore ends on their 70's to a female threadded bushing but also on their first 3 versions of the Model 52 smallbore match rifle. They finally got rid of it on the 52D and 52E versions.
I doubt it was the bullet quality. Winchester-Western's 180-gr. FMJBT match bullet shot as good as the military 172-gr. FMJBT match bullet; about 7 inches at 600 yards with the best lots of each in the '20's and '30's They did that in M1903 Springfields and Win. Model 54 based .30-06 target rifles with free floating barrels. The 1924 .30-06 National Match ammunition was one of the most accurate match cartridges ever made, giving a 600-yard mean radius of only 2.26 inches from an M1903 (about 7 inches extreme spread), a record that would last until 1962.