On a good note, my wife had minor surgery in Hungary once. I filed it with my US carrier and they didn't reject it, but the cost was less than my deductible. In the States would have cost many times more than the deductible. At least it went towards fulfilling my deductible. I get my dental work done there and buy prescriptions there for less than the covered cost in the States. So what you need is coverage for the big ticket occurrences. I have a policy for that and evacuation, etc which I found to be cheaper to buy on an annual basis than by the trip because I usually go 3 times a year.
As for the person in the story, would have been the same in the US with no paperwork to support the claim. Had nothing to do with the insurance company. I see a doctor in the US that refuses to process insurance, I have to file it myself and for that I need a diagnosis, treatment and receipt. Common sense.