According to a couple sources I just checked via a quick Google, Americans actual own ~3 times more guns per capita than Canadians. 31/100 vs 89/100. Switzerland is ~25-46/100 - military rifles kept at home included. Not sure why the range in that figure.
In my mind it would be interesting to know the numbers when you start counting handguns. I suspect the difference would be much more dramatic.
In Switzerland the guns are kept at home, but only 2000 specialist militia members are allowed to keep military issued ammunition at home. The rest have to go get their bullets from an armoury when the time comes... I don't know what Switzerland's ammo control laws are.