I watch a lot of asian media, espeically from Korea. Koreacare is a lot better than Sovietcare, which I saw first hand. But one of the recurring memes from Korea, Japan and Taiwan is that rich folks, even doctors, arrange to have their non emergency care done in the US.
Part of the reason of course is what is required of the patient and the family at Aisan hospitals. The patient's family is expected to provide meals and do laundry and to have someone there all the time. Family members are even expected/allowed to be there overnight, and there are cots provided for them, in order to take care of bathroom and other issues.
Also, Asian hospitals have a co pay. In Japan, the first 5,000 is the patients responsibility. The government will cover anything over that if asked. Of course, if the government is paying for it, you get it on the government's schedule. So those who can afford it either go to the US or pay extra at home.