And many doctors will tell you about the miracle healings when people pray, healings that they have no idea why they came about.

Sometimes, the human body is able to fight back the viruses and bacteria which causes the diseases. This immunity varies from person to person. It has nothing to do with prayer or religious belief.
I do believe that religion is harmful to health. A lot of religious tenets aimed at the fact that the best medicine is prayer. This leads to the fact that people later go to the doctor and die.