In addition, based on my past (sometimes failed) attempts to claim back money for illnes from from private travel insurances, I would trust the Swiss Krankenkasse explicitly for paying out. In the UK I was with Bupa (paying more than my current Krankenkasse) for a few years until I actually had to use it - they tried every excuse to worm out of full payment. Maybe I am one of the only fans of the swiss system ?