Hathir,
all of the research I did stated that Saudi Arabia provides free health care:

"Saudi Arabia has committed vast resources (US$16.4 billion in the years 1985 to 1990) to improving medical care for its citizens, with the ultimate goal of providing free medical care for everyone in the kingdom. In 1990 the number of hospitals operated by the government and the private sector together stood at 258, with a capacity of 36,099 beds. Of these hospitals, 163 were run by the Ministry of Health and sixty-four by the private sector. There were also thirty-one teaching hospitals attached to the medical faculties of universities in the kingdom.

King Fahd Medical City outside Riyadh was a US$534 million project. It was to include five hospitals of different specializations, with a capacity of 1,400 beds in addition to outpatient clinics, and was expected to be completed in the early 1990s. To provide personnel for the expanding medical facilities, which in 1992 were staffed largely by foreign physicians, nurses, technicians, and administrators, the government has encouraged medical education in the kingdom and has financed medical training abroad. Four of the kingdom's seven universities offered medical degrees and operated well-equipped hospitals. Saudi universities also had colleges of nursing, pharmacology, and other fields related to the delivery of medical care.

One objective of medical planning was to sponsor cutting-edge research in the kingdom. There were some reported successes. The King Saud University College of Pharmacology developed a drug effective in stabilizing blood sugar in diabetics, and heart surgeons at the Armed Forces Hospital Heart Center in Riyadh performed innovative open-heart surgery on an infant. At the College of Sciences of King Saud University, scientists have used radioactive isotopes to determine the effect of antibiotics on body functions. The King Khalid Eye Specialist Hospital, staffed by foreign doctors, was a world center for the treatment of eye disorders.

Whereas advanced medical research and some of the most sophisticated medical care available anywhere in the world were concentrated in Riyadh and a few major cities, medical care at the most basic level was limited in the countryside. In the early 1990s, a key objective of the Ministry of Health was to facilitate the delivery of primary care to rural areas by establishing primary health-care centers that provided basic services and dispensed medicines. For every four or five primary centers, which numbered 1,668 in 1990, there was to be one diagnostic and maternity center (there were ninety-eight centers in 1990). The large specialist hospitals located in cities were intended as referral hospitals for sophisticated medical treatment such as transplants, cancer treatment, surgery, and complicated diagnoses."

Source: U.S. Library of Congress