Individual mass produced bolt action rifles can often be very accurate. Finding the right load is usually the secret. Assuming a good trigger pull, properly fitting stock, a good scope in properly tightened mounts and rings, shooting off a solid shooting rest. Its usually possible to get most any bolt action center fire rifle to shoot a sub-2 MOA group. I consider 1.5 MOA my own personal minimum hunting standard, its usually not hard to find a load that will achieve that.
I've seen the least expensive old Remington, Winchesters, etc shoot sub-MOA groups. Its amazing what handloading can do. Often times one half grain of powder is the difference between sub-MOA and 1.25 MOA. Conversely there are rifles that one could try ten different powder, projectile combinations and never break 1.75 MOA.
Then there is natural loss of accuracy as the barrel wears. For example I had a custom built .270 that would make one 1/2"-3/4" 10 shot hole at 100 yards when it was new. However after less than 2000 rounds it started losing accuracy and opening up those groups.
Now then, in terms of reality and the average shooter. If someone claims there old beat up rifle will shoot sub-MOA groups with factory ammo, while they are leaning across their truck hood and using a rolled up jacket for a rest. Well, lets just say I'd have to see it, to really believe it.
a lot of it has to do with the skill and knowledge of the owner, but yeah, some mass produced rifles will shoot sub-MOA.