Switzerland is very special for multiple reasons. They have a direct democracy, federal system with very small cantons (equivalent of states) and until very recently every mail had an assault rifle at home. They're also very law-abiding citizens in general with >80% of crimes being commited by immigrants. I like swiss model a lot, but it's not 100% clear it can be scaled to a bigger country or if you need centuries of public awarness (they never had a king for example). The differences are so big, it's really really hard to compare with any other country.
All true and I admire Switzerland for all those reasons. However, at least some aspects of the "Swiss gun culture" actually exists in the U.S., among enthusiasts, who have a serious "culture of responsibility and safety" and teach their kids the same. Go to, say, a competitive shooting event, and you'll get an entirely different impression of gun owners than you may have now. As someone in the Time article says, "If people have a responsible, disciplined and organized introduction into an activity like shooting, there will be less risk of gun violence."
For the patriotic side, check out Project Appleseed (http://www.appleseedinfo.org/), which conducts weekend courses on rifle marksmanship and Revolutionary War history. (It's run by volunteers, and costs $70 for a weekend.)
This culture used to be more widespread in the U.S., back when rifle shooting was a high school sport. The more we crack down on legal gun ownership, the more we stamp it out.