There are a lot more factors then just the technical that play into how many you shoot to 'test'.
To start off there is purpose as others have stated. A big game rifle the 1st cold barrel shot it the one that counts, and sometimes the 2nd, and almost never the 3rd. The Ol' hunter saying, "0ne shot, dead deer; two shots, maybe deer; three shots, no deer." So for a big game rifle I see no problem with three shot groups as long as you can do them from field positions.
Varmint and target rifles have different demands on them and should be developed and treated as such.
Now the real factor is for any group you have to know what you are measuring. Are you measuring the rifle / load combo or the shooters ability. I have shot a fair number of sub one inch groups in my life with five shoots, but never been able to do it with ten shoots. This is not the rifle or loads fault but mine as a shooter. I have my rifles for hunting and fun (plinking) and I am not a target shooter.
To give a real world example I have a Marlin 1895GS 45-70 lever action. Now no lever action is 'easy' to test from the bench. If I start out try to test new 'hunting' loads the first few targets are all over the place regardless. Now if I warm up shooting with some mild plinking loads and get myself settled in with the rifle first, then those hunting loads targets start to mean something.
Remember the shooter is a 'BIG' part of the test here. Now if you have heavy recoiling rifle, how well will you be shooting on shot number 10 to 12 lets say.
The bottom line is that it all depends. Not that what you read was wrong, but rather that it just is not an absolute in all cases.
This is the long way of saying what is important is .... Can you hit what you want when you want with the rifle / load combo ???
If the answer is yes you are fine. If the answer is no then you need to work on it.
Let us stay focused on the purpose and use only the details that get us to where we want to be.
