It’s a myth. Quality ammunition in a quality firearm is what matters. One caliber is no more accurate than another
No, not at all a myth when you get to Benchrest precision levels. It's not just what the cartridge itself can do, but how it interracts with the firearm and the shooter in terms of dynamic stresses and movements on the barreled action, recoil and torque effects etc. As a result, the larger the cartridge the harder it is to
consistently produce very small groups. Note
consistently. Serious students of rifle precision have less interest in one-off tiny groups than in averages of group series. That's why all BR matches results and league placings use match aggregates (Aggs in the vernacular), actually an average, of the four or five groups shot over the fixture.
As others have said in their posts, the 6PPC has proven not only outstanding, but unbeatable, over what is now 30 plus years in short-distance BR. There have been many attempts to knock it off its perch, but so far none that has managed. If you consider the Remington BR appeared around the same time and was designed to be the ultimate in short-distance precision, it never got off the ground in this role due to an unlucky timing coincidence with the PPC's emergence. Yet, most people would consider the 6mm version of the BR an outstanding precision number, which it is. It's probably just a little too big and over-powered to be top dog in 100/200 yards competition, but it and its improved versions are winners in 600 yard, often 1,000 yd BR too, competition, especially the 'improved' Dasher version. It was confidently predicted that the 6mm wildcat variant of the 6.5X47L would see the Dasher off with just a tad more case capacity and able to hit the next speed node up, but that never happened and many precision shooting experts reckon that's at least partly because any performance / charge weight increase over the Dasher produces more downsides (shooter controllability, recoil management, speed of shot series, barrel movement etc) than the relatively small performance upgrades.
When Remington's 40 series competition rifles from its 'Custom Shop' department were around the best performers money could buy, each rifle was delivered with a target with a benched group proving that the individual rifle performed as advertised. Remington Custom Shop people kept the group records and ended up with many years worth of aggregate rifle and cartridge performance. The smallest average came from 222 Rem chambered examples; the largest from 300 Win Mag examples, and there was a straightforward correlation between cartridge and charge size v groups - bigger the cartridge; bigger the average group.
Also, as a rule, increasing the cartridge capacity to bore area ratio value not only increases barrel wear, but also usually makes it harder to achieve ultimate precision, in particular a lot harder to produce good performing load combinations that behave consistently and with wide 'accuracy nodes'. This appears to be the case with the 6-6.5X47mm Lapua. Necking the 6.5X47mm Lapua down to 6mm increases the ratio from 873 to 1,043. (The 1,000 mark is often reckoned to be the approximate borderline where a cartridge starts to be really hard on firearms.) The 6BR's ratio is 822, and the 6PPC's 717 by comparison. Some people have got the 6-6.5X47L to shoot very well, but many more gave up on it after getting excellent results on some occasions that wouldn't then repeat consistently. It's a very minor player these days in any and all shooting activities.
As to it being simply about rifle build and cartridge preparation, the best example I saw disproving that came from Ken Waters' writings for Rifle and Handloader magazines in his 'Pet Loads' series that ultimately ended in decades of testing and reports and many, many scores of cartridges. Ken dabbled in short-distance benchrest and being around on the scene when the PPC swept the game over a mere two seasons, reckoned it was more to do with fashion and follow the leader than true precision. The top dog prior to the PPCs was the 6X47mm (6mm-222 Rem Mag) and Ken had top BR gunsmith Seely Masker build him a state of the art, no expense spared, bench gun in that chambering, ran it in and undertook a comprehensive load testing and development programme. It shot well, supremely well by most standards. Masker then took the barrel off, set it back a bit and rechambered it for 6PPC. It shot better, much to Ken Waters' surprise and chagrin as he admitted in the features he wrote about this experiment. Tenths of an inch group sizes better in a discipline where thousandths of an inch 'agg' difference often determines the winner and also-rans.