I'm curious where you're sourcing your information. To my knowledge the management team is made up of administrators from multiple countries of which the US is one. That would not be unusual for any institution seeking international credentials, investors and staff. That there is a McDonald's on the premises indicates nothing. That restaurant is a locally-owned franchise as are all McDonald's in Thailand. I hope you wouldn't suggest that by their presence in the county that Thailand is "owned" by the US.
Perhaps be a bit more careful with your "facts". Bangkok Dusit Medical Services, the owner of Bumrungrad 1 Hospital, is Thailand's largest private healthcare group. It was founded by the Thai billionaire Prasert Prasarttong-Osoth.
You're not the first to assume that my given name has anything to do with what I do or do not believe. Aside from that intended slight, references to health insurance from expats have nothing to do with the worthiness of travel insurance for travelers. And no one would argue that there are cheaper alternatives to private hospitals in Thailand, but as I noted many, if not most travelers would not be aware of those differences nor might they be in a condition to have a say in the matter.
Larkin for pointing out the wisdom in purchasing travel insurance before embarking on a trip. By definition an accident is never *planned". And most travelers won't have the choice or the presence of mind to choose which hospital will treat them. For most travelers the cost of travel insurance is a small fraction of ones travel budget. Here's wishing your wife a full recovery from her injury.
I don't know if the system is sophisticated enough to track your IP address, but the requirement is that one apples from ones home of record (in your case, the US). You can most certainly complete the application from Cambodia and it's possible a VPN will shield your location but with a non-refundable $200 fee you might hesitate at taking a chance.