Yes I meant people with private health insurance, who pay on top of or indepent of whatever national scheme their government has. For people from Germany and Netherlands for example this insurance would be about 35-40% of the Swiss cost.

I assume it is only for new arrivals, as you have to do it within the three months although if you are energetic you can always go to the kanton with the EU card and ask (say just before the end of your yearly Swiss insurance is renewed). But don't call, you are not likely go get far on the phone I think.