People in the operating room pay attention to a rich patient's wishes because they know a rich person can make their lives miserable. He can complain to the hospital president, or call the mayor. But the side effect is that their high quality care becomes habitual, and all patients receive it. When a poor person complains in most environments, no one listens. But in health care, through a common private insurance system, poor people go to the same hospitals and doctors as rich people and thus enjoy the benefit of rich people's power.
The public option severs this link. Dissatisfied with government-run health care, the rich will exit the system. The poor and middle-class will be left to flounder alone inside the public system. Government-run health care will become like the public schools.