That worked for my trip to Brazil last year, but not when I tried for Cambodia. They just couldn't get the two or three specific requirements in one letter! In the end, I booked FORTE (Cambodian company, so their insurance fits the requirements exactly and is known by airline and immigration staff).
I have no health insurance now, when I go to Thailand I will probably take AXA as will be the smoothest (Thai company, known by airline and immigration).