In my experience, the only way you can get away with not having Swiss health insurance is if you are officially employed as an expat (not sure how this is defined, but hey). I'm moved to Switzerland with my fiancé, who was moved by his company, and therefore is expat. As I was taken on locally, my EU insurance (which was more comprehensive than the local swiss insurance) was thoroughly irrelevant.

I fought for a long time on this point, but in the end, I had no option but to take on local insurance.

However, if anyone finds a loop hole for locals, please do let me know, as I'm not particularly impressed by my insurance...