What about Medicare?
Medicare is a government-sponsored medical insurance program administered by the Health Care Finance Administration (HCFA). It is generally available to persons age 65 and older. It is also available to people under the age of 55 if they are disabled under Social Security for a period of at least two years. (I may have over-simplified these facts somewhat--consult your Social Security Office for the exact details.)
Since the age of transplantability generally tops out at 65, for a 65-year old person not disabled under Social Security but needing a transplant, Medicare is basically a non-issue. There is the possibility that some medical insurance companies may require the transplant center be Medicare-approved as a basic Quality Assurance measure, but I expect this is rare.
For patients that are under 65 and approved for disability under Social Security but have not yet been disabled for the required two years to be eligible for Medicare, Medicare approval is again not the major issue it might seem to be with respect to selection of a transplant center. This is usually because most respiratory diseases requiring a transplant are aggressive, and don't sit around waiting the required two years for the patient to qualify for Medicare before it is time to be transplanted.
After the transplant, Medicare can become more of an issue with respect to medical insurance coverage if the patient does not return to work. By this time, a patient disabled under Social Security would have been disabled for the required two years, and automatically be notified of Medicare eligibility. Then the fun of finding a suitable Medicare supplemental insurance policy begins, but that's a subject for another website--stay tuned for that one.