Just a general tip for all out there, get legal insurance! for only a few francs you can seek out legal representation on all manner of issues. I have coverage for employment, car, renting and general issues. A letter from a lawyer often encourages the 'big' companies to take you into consideration. Without they dictate their small print to you.
Not sure about the health insurance - if you cancelled in writing, sending it registered mail as proof. It is then up to them to ask for further information etc. If they didn't I would show up at the betreibungsamt and contest their demand.
Having been at a Betreibungs incident - on the money owed side - they are quite fair with the evidence presented. Sadly, not knowing doesn't prevent you from loosing.