Earlier quoted context omitted.
I'd say that the key difference is that Switzerland has compulsory military service in which you're taught how to operate a weapon properly. Therefore, everyone that has one has gone through months of training. Vs the US, where there are loopholes that you can use to avoid even a basic background check, and then use it for the very first time to shoot someone.
Training seems likely to cut down on accidental shootings, but not so much on the deliberate ones.
Second, you learn a certain respect for the firearm and are expected to observe strict safety rules when handling it. That gives you a kind of psychological flinch when you consider doing anything out of the norm with it.