The secret to good health is the maxim "Know Thyself."
When the funding for health care comes from a third party, people are reduced to following strategies that can obfuscate the knowledge that would help them live happier, healthier lives.
For example, people will try to hide pre-existing conditions from insurers when they apply for plans.
People (sometimes in collusion with their doctor) are tempted to overstate illnesses when they make a claim to get full benefits.
When a person is dependent on a third party (be it public or private) the strategy the adopt to deal with the third party distorts the knowledge they need for optimum health.
Even worse, in efforts to control costs, a third party payer might block access to information that could really be helpful to an individual. As mentioned earlier, the paperwork follows the payment. Doctors and insurance companies share information that the patient does not see. In third party payment systems (like Obamacare), there is valuable information they might miss.
Conversely, when health care is self-funded, people have a direct and immediate incentive to learn about their health. People who self-fund care will want to know everything they can about expected expenses and preventative medicine so that they could control costs.
This issue comes to light with things like emerging genetic science. The self-funded person would be eager to know if they have a pre-disposition to any genetic disorder. The info would help them in budgeting. In a system of third party providers, this information is something that could cause a person to get cut from the role if the genetic malady was discovered by the provider.