In reply to JJL: Air Zermatt billed me about £1,500 for a straightforward airlift (no searching etc). That was 12 years ago so add on a bit for inflation and the crap exchange rate.
The overnight stay in Visp hospital was £2,000.
You might be lucky however, some friends were airlifted in the Dolomites once and were never charged. They had insurance but nobody asked to see anything or even took their names and addresses.