I would assume the Swiss have received the necessary firing weapon training (which surely comes with a lot of safety measures drilling) which could have an impact.

I would also assume that the Swiss don't just allow anyone to join the military and thereby obtain an assault rifle, but that there is some psychological screening, that would prevent an unstable person from joining the military.

Meanwhile, in the US such a person just walks up to the gun shop and buys a firing weapon.

Because in Switzerland people have guns to defend the state from invaders. In the US people have guns to defend themselves (from the state or other people).

Also in Switzerland people store their military service gun but they don’t have bullets.