Patient records are private information, and only doctors who need to see them for medical reasons should have access to them. If the government has access to patient records, there is the danger of them falling into the wrong hands. It's important to keep them away from companies that might use them for marketing purposes.
The fundamental unit of healthcare is the interaction between doctors and patients. There exist scenarios that require one doctor/ one patient, one doctor/multiple patients, multiple doctors/multiple patients or multiple doctors/one patient. Just like how cells in our body perform individualized tasks which manifest into a harmonious system, this is how I view the health care system. If decisions for each unit are transferred to centralized administrative levels, the problems in health care today will be confounded. If doctors are allowed more freedom to act with their units, then an organic system will manifest itself with less administrative cost (i.E. Liability, limits on coverage, patient records, etc.). There are amazing technological advancements being made in the medical sciences, but these applications are already limited by dysfunctions in health care administration. Government-run health care is not a solution in my opinion, because it transfers the decision-making powers of doctors to another type of administration which does not specialize in medical care to begin with. To optimize health care, there must be universally affordable coverage, digitized records that can only follow the patient, and decreased liability costs. Each factor becomes a problem if health care is overseen by lawmakers. More oversight will explode liability costs, which will make risky procedures even more expensive (so much for affordable coverage), and allowing government administration to access patient records will inevitably lead to leaks in information that could be exposed to political opportunists.