You don't know that. By definition it will not have happened if it was prevented. The point is not that you will start shooting. Rather it's that you could.
Moreover there's a fundamental issue in the US that quite a large proportion of the population supports what is going on. This varies by location of course but that just exacerbates the issue - there are places in the US where the vast vast majority of people have no objection to what is happening.
I didn't say "it's working" I said "you don't know that it's not working". It's a claim that your logic is faulty. I then proceeded to outline a plausible theory which conflicts with your claim.
The example fails for the same reason. There's no way to rule out the possibility that there would be more rights violations in said countries if people possessed fewer arms on average. There's also no reason to expect violations to go to zero, only for them to be deterred to some extent on average.
It's similar to the MAD doctrine. That doesn't predict no war, just less war and smaller wars in general. It doesn't even predict no use of nuclear weapons, merely that any use is rarer, more judicious, and more deliberate.
Moreover there's a fundamental issue in the US that quite a large proportion of the population supports what is going on. This varies by location of course but that just exacerbates the issue - there are places in the US where the vast vast majority of people have no objection to what is happening.