If you think we have problems in the US, you should try Greece.
There had been talk of a socialized system several years and a couple of prime ministers ago. There seems to be a modicum of a centrally funded, insurance-based system now. However, the WHO's description of Hellenic healthcare tells me it still runs the old-fashioned way:
[Informal payments] are especially prominent in the case of in-patient care, and are made to doctors, mainly surgeons, in public but also in private hospitals. These payments are also made in the case of outpatient care. The rationale is to jump the queue or to secure better quality services and greater personal attention by the doctor. Unofficial payments are considered to be a major problem in the Greek health care system. It is estimated that about half the total private expenditure on health care involves informal payments. There is no really reliable estimate of the size of the unofficial market, partly because it is so widespread, and partly because of the complexity of the Greek health care system.
Almost 60% of total out-of-pocket payments (official and unofficial) are made to doctors and dentists, 20% go toward pharmaceuticals, with the rest being mainly expenditures on private diagnostic centres and private clinics. Out-of-pocket payments (both official and unofficial) represent roughly 6% of household income (1990 figures).
So these informal payments are made under the table, usually cash stuffed into an envelope and they are fairly common, even in the out patient arena. Traditions die hard, and the tradition of the "fakelaki" (the Greek word for envelope) is alive and well. I believe these payments are outlawed in the government-run clinics, but common prejudices take effect: Greeks are nearly Italian in their disregard for authority and let's face it, doctors can't be any good if they works for the government! You and I may know it's not true, but there's no accounting for consumer decisions.
My suspicion is that the lowest risk way of buying a stake in Greek Healthcare is to buy a stake in an envelope factory.