It's only one data point, but I thought I'd share.
The wife and I went to Maui this summer, and she booked the trip through her Avion Visa card, which includes added medical coverage.
Anyhow, on day 2 of the holiday, I thought I'd spice things up by taking a header into the sand and fracture my neck in 3 places. (As anyone knows, this could have been a real game changer for me and my family. I'm REALLY FUCKING LUCKY that there was no nerve damage and I should recover fully.)
When I landed on my head, I was quite confident that I'd done some damage. I consulted with the lifeguard, sat down for a minute, then decided I'd best seek medical attention. I was boarded, hauled off the beach, and put in an ambulance. (Just over US$1200 for the 20 mile trip, btw). When I arrived at the hospital, they were asking about insurance right away. My wife arrived shortly thereafter, and had already called the insurance # for the credit card. Things progressed smoothly from there: I was given a CT scan, met with the neurosurgeon (no surgery needed), set up with a neck brace and copies of my scan and the reports to take home, given some meds, given a care plan, and discharged in not much more than two hours.
I expect that a majority--if not all--of the expenses will be covered by MSP and my extended medical at work, but being able to call one person and have them sort everything out was a real bonus in the midst of a crisis. They called back the next day, the day before I left (we stayed for the remainder of our week--if you're stuck sitting around, might as well do it in Maui instead of the Fraser Valley), and after I returned home. Everything was seemless, and any questions/concerns were handled quickly and efficiently.