Maybe we should change the title of this thread to:
Very cheap Swiss health insurance for students and researchers

Based on the discussion on this thread, I looked into the student health insurance further and it does appear that researchers, including post-docs can have the student health insurance and thereby save themselves a LOT of money. I had always ignored the student insurance before because anything else that applied to students did not apply to me as a post-doc. However, it appears that health insurance may be the exception to this. I just filled out the forms online at SwissCare and they have sent me something to send to my canton to get it all officially sorted out. I highly recommend that researchers in a similar position do likewise, but I expect that they won't read this thread unless the title is broadened to explicitly include them (which is why I had previously ignored it).