Lone Star,
You say your "hobby" is pinning down some of the shooters who claim very tiny groups from their firearms on a regular basis. You offer to buy their ammo and pay their range fee if they come to your range and show you. You "call their bluff". With all due respect I find that a strange "hobby". I've looked at many of your last posts and I don't see any real challenges issued - just snide inuendo, not really directed to anyone. Maybe I just didn't read enough of them, or you do this on other forums.
I sincerely and respectfully find it amazing that anyone would care enough about what you think to feel that they had to prove anything to you. You have stated (correctly, I might add) that it's easy to claim small groups by using a keyboard, or something to that effect. I guess I would add that it's equally easy to claim that shooters would come out to a range and perform for someone because of some cyber-challenge and the offer to buy some bullets, or ammo. It also seems counter-intuitive that a BS'er would answer this challenge anyway if he didn't feel he could do it. Conversely, if he did believe he could do it, then he wouldn't be a BS'er, so what's the point?
Now if you say this is your "hobby", and people actually do this, I won't doubt you. Let me just say, well, I think it's amazing.
But back to shooting and accurate barrels: You have stated that (condensed version) that unless one uses a machine rest one must shoot it himself, a few moa groups don't mean the firearm is capable of doing it consistently, and even a machine rest can result in group sizes that vary consiiderably. OK, what I get from all that is that the firearm/ammo combination either shot from a machine or by the shooter can vary a lot, and we cannot claim an accuracy level without shooting enough to demonstrate its accuracy.
In general, those statements are theoretically correct, but they are not precise or measurable, just stating the obvious.
So, what is your exact statistical criteria for a barrel/ammo/shooter combination to claim an accuracy level, and is there some standard which is universally agreed upon? I do believe you are very knowledgeable, so please share with us.