Can John Rawls' Theory of Justice be applied to U.S. healthcare reform without violating HIPAA laws?

John Rawls highlights two central principles about equality in his book A Theory of Justice:

One, that each person should have equal rights to the most extensive liberties consistent with other people enjoying the same liberties; and two, that inequalities should be arranged so that they would be to everyone’s advantage and arranged so that no one person would be blocked from occupying any position. 

If legislatures adapted them as part of U.S. healthcare reform, it does not seem like these principles would violate personal HIPAA laws. The reform would most likely result in a universal healthcare model and truly affordable healthcare for every individual. It could even create a “pay what you can” model, entrusting citizens to intuitively and fairly create their own pricing for doctor’s visits, surgeries, or other emergencies. What an individual decides to pay in this model and what care is provided is still private and upheld under HIPPA. Rawls’ Theory of Justice would definitely be a complicated puzzle to apply to healthcare reform, but its core tenants do not seem to violate individual freedoms and the right to privacy.
https://www.hhs.gov/hipaa/for-professionals/privacy/laws-regulations/index.html