A man goes to heaven and is being given a tour of the grounds. While visiting the hospital cafeteria, he witnesses a peculiar scene. A big man with white hair and a beard, dressed in scrubs and a surgical mask, barges into the line and pushes his way to the front, demanding that people get out of the way because he is so important. The new arrival says to his guide, "What's that all about?" The guide responds, "Oh that's just God. He likes to think he is a surgeon."
I know a slightly different version of that story, but a physician (who is not a surgeon) assures me that this version is more authoritative in the medical community.
The point of the joke is the point of the word, "rofei." It means "healing" or "curing" and in both secular society and religious thought it is mixed up with God-like powers.
In English we make the distinction between curing, that is, doing away with an illness or injury, and healing, that is reconciling with illness and injury. Hebrew makes no such distinction. Our plea to God, articulated by Jeremiah, is "r'fa'eini adonai va'eirapei," "heal me, God, and I will be healed." It finds its way into the daily Amidah phrased, as all the brakhot are, in the plural. We know God is with us when we are cured.
Of course, we do not presume that sickness is abandonment by God. But for a very long time sickness much more frequently led to death than it does today, and illness or injury was (and is) indeed seen as a limiting factor in appreciating God's presence by most. (It is the spiritually healed person whose perception of God is enlarged by physical compromise.) So if sickness is the prelude to death, then healing is the triumph over death. Referring to God as "healer" or "doctor" in the same blessing that affirms God's power over death is entirely consistent.
It also renews our appreciation of the task of doctors and other health care personnel as partners with God in this sacred work. Especially surgeons!