...the OP’s gun probably shot better the he did. ...
I have guns that can shoot better than I can. I have some guns that won't shoot as well as I can. I can demonstrate this fact by shooting smaller groups with a more accurate gun than the other gun can shoot when shooter error is eliminated.
For example, I have one autopistol (let's call it pistol A) that won't group better than 5-6 inches at 15 yards, even with shooter error eliminated/minimized. But I can demonstrate that with another pistol (pistol B) , I can shoot offhand groups of 3" at 25 yards (admittedly with some warmup and a maybe given a few attempts at it). So in that case, pistol A certainly doesn't shoot better than I do. Pistol B probably does shoot better than I do since there is some shooter error in the offhand groups.
The accuracy of any gun is the sum of multiple factors; let’s call them errors. Two of the most important are the inherent mechanical accuracy of the gun as determined from a fixed rest and the errors by the shooter.
The accuracy of the gun has nothing to do with errors by the shooter. Errors by the shooter are the accuracy of the shooter.
2" off the rest. 5" offhand. That means (I think) 2" mechanical error and 3" shooter error.
It's a little more complicated than that. Both shooter error and firearm error are random in magnitude and direction, therefore it's not possible to simply sum the average group sizes and get the correct answer.
A reasonable approximation/estimate for the combined error can be obtained by summing the squares and taking the square root.
So with a shooter capable of shooting 3" groups and a gun capable of shooting 2" groups, the combined accuracy should produce groups that are about 3.6" in size.
However, that's mostly moot as combining shooter error and gun error to try to assess the accuracy of the gun is problematic. The accuracy of the gun needs to be assessed with shooter error eliminated, or at least minimized to the extent possible.
The main reason the gun is more accurate than you can shoot is that your shooting INCLUDES the error inherent in the gun.
We can assess shooter error and firearm error independently of each other (well nearly so anyway) by shooting the firearm from a rest or fixture, and by assessing shooter error with a very accurate second firearm. Then we can compare the two to see which is smaller. In the example I gave, I can show that even with shooter error nearly eliminated, pistol A can't make groups at 15 yards that are as good as the groups I can shoot at 25 yards with a more accurate gun. Therefore my accuracy is better than pistol A. Pistol A does not shoot better than I can.
Now, if we assume that I can only assess my accuracy using pistol A, then that's a problem. HOWEVER, even then we can get a rough feel for things. Let's say I shoot pistol A from a fixture that totally eliminates shooter error. Then I shoot pistol A offhand at the same distance and with the same ammunition. If my offhand groups are very nearly the same size as the groups shot from the fixture, that pretty much says that the error due to the gun is dominating the results, even with my error combined into the equation and that suggests that I could outshoot that pistol A with a much more accurate pistol.
If we were both contributing about the same amount to the error, the groups shot from the fixture should be noticeably smaller.
But does that mean the gun could not and should not be improved? Would the overall precision not be better if the gun were better?
It depends on the shooter. If the shooter is not capable of shooting better than 8" groups at 7 yards, then spending the money to buy a gun with a 1.5" accuracy guarantee at 50 yards is probably not warranted. If the shooter WANTS a really accurate gun, then that's one thing. If they buy it thinking that it's going to cut their group sizes at 7 yards, they're going to be very disappointed unless their previous firearm was very inaccurate.
Here's an example. Let's say that the shooter has a gun that will shoot 4" groups at 25 yards from a Ransom Rest. That works out to groups of about 1.12" at 7 yards. If the shooter is getting 8" groups at 7 yards with that gun, then we can calculate that the shooter's contribution to the overall group size is about 7.9212"
Square Root (7.9212^2 + 1.12^2) = 8.0000"
The shooter is unhappy with 7 yard accuracy and buys a gun that has an accuracy guarantee of 1.5" at 50 yards. The new gun can shoot groups of about 0.21" at 7 yards with shooter error eliminated.
Square Root (7.9212^2 + 0.21^2) = 7.9240"
The improvement in groups at 7 yards due to the more accurate gun will be less than 0.08". Groups will still be about 8" at 7 yards even with the much more accurate (and much more expensive) gun.
I agree that there's a tendency for people to rush to judgement when someone complains about accuracy and automatically assume it's shooter error. You really need to have some idea of how both the gun and the shooter perform
independently before it's possible to make an accurate assessment.