There was a time when most gunwriters were familiar with, or competed in, NRA rifle competitions. The typical group is either 10 rounds, for rapid fire sitting and prone, or 20 rounds prone long range. If you shot small bore prone, you shot 20 shots for record on each target, though that is four 5 shot bulls at 50 yards and two ten shot bulls at 100 yards. There are good reasons to spread the shots out in small bore, it becomes impossible to distinguish between hits at greater shot counts.
So, there was a time when you expected to shoot 20 round strings, and shooters understood that consistency was a quality attribute. It is also very hard to shoot a 1 MOA group, or less, with 20 shot groups, or even 10 shot groups. Inaccurate rifles and ammunition combinations simply cannot shoot tight, high shot groups.
The idea that a "bad" shot is just as likely as a "good shot" assumes that each shot will have the same potential offset from the center. I do not believe that is true. When you are talking about normally distributed groups, shots far away from the mean would be things that have a chance of 1:100, or 1:1000. You have to fire enough shots to determine a meaningful mean and standard deviation, but remember ,
68% of the distribution lies within one standard deviation of the mean.
95% of the distribution lies within two standard deviations of the mean.
99.7% of the distribution lies within three standard deviations of the mean.
Small shot groups are less likely to pick up a three standard deviation data point.
While it is true that lightweight barrels start to "walk" once they heat up, that does not preclude waiting between shots for the barrel to cool down. Given enough cooling time, even a ten or 20 shot group can be fired from lightweight hunting rifles, which would provide a much better estimate of the true accuracy of the rifle, than three shot groups. Two points define a line, three a plane, but three shots do not determine much of anything else.
I can say even five shot groups can be deceptive. I have been running tests on my FN 270 Win, developing loads with five shot groups, and if they have promise, shoot large groups to test the hypothesis. Recently I shot a really nice tight five shot group with 130 Fed Fusion's and WC852. I really thought I nailed it. Then I shot a 20 round group with that load. Not awful, not great, nothing to crow about. Now, if I had left well enough alone and not shot that 20 round group, I would not have learned the load was so-so, but I would have been happy living in my delusion.
It is my opinion that the three shot groups that gunwriters publish reveal little to nothing about the true accuracy of the load, or the rifle. One very prominent gunwriter shot three shot 30-30 groups, out of his lever action Marlin, most I think were cast bullets, and the guy was claiming sub MOA groups. I am of the opinion that this is the Texas Sharpshooter fallacy
http://www.fallacyfiles.org/texsharp.html. This gunwriter does not have a sub MOA Marlin, he has not fired enough shots to shot the true accuracy of the thing. A competitive shooter would know that accuracy comparisons based on three shot groups would be totally spurious, because he had shot enough groups to know that three shots are not enough to determine whether a load is accurate, or just a statistical fluke.
There are a number of good reasons why gunwriters don't thoroughly wring out firearms under test. The first is that it is a lot of work. The second is that a through shooting test might reveal that the firearm is a dog, something which the advertiser does not want to be known, (it is just as likely that the gunwriter is not a very good shot anyway) Plus the fact, that gunwriters are not compensated because they can shoot small groups, future commissions depend on the sales bump his article provides now.