It has everything to do with it. The "Swiss model" is exactly what the Founding Fathers had in mind with the Second Amendment. No standing army, and organized state militias. They probably have the longest-standing militia in existence, from the days of cross-bows to todays assault rifles. The FF also had in mind the Republic of Venice, which was similarly organized.
I’m not sure I agree. Outside of the Swiss concept of the Militia, does a Swiss citizen have the right to keep and bear arms? Here, I have an individual right to keep and bear arms that has nothing to do with any militia. At least that is what the Supreme Court said last year.