To clarify the insurance I bought was underwritten by a US-based company (I forget which one now.) There are many policies like Patriot USA or some such name that are sold. And the policy was fairly expensive but my experience with it was mediocre. Similar travel policies can be bought overseas (by the guests themselves before they arrive in the USA) and which are considerably cheaper. I am leaning towards this option in the future. The more expensive US-based policy didn't buy us anything more.