The death rate per doctor goes up because the number of practicing doctors is going down and the number of really sick and aging patients every doctor sees is continually going up.
Suppose you were Dr. Wm. Tell, a brain surgeon whose specialty was removing apples from patient's heads with a target rifle at 30 yards. You are among the best in the country and do 500 of these procedures per year, because patients who truly need the procedure trust you and come to you for the service. Some have smaller apples than others. Some can't hold still and tend to move during the procedure. And you aren't always able to pick and choose who gets treated and who doesn't. How often might you have an unexpected "accidental death", no matter how careful you were and no matter how good a shot?
I take Gene's post in the context it was made, light hearted sarcasm, the point being that when properly handled, guns are as safe or safer than, say, high-risk medical care, or lawnmowers, or slippery slanted surfaces around the home or shop. But physicians are neither god-like nor perfect in performing procedures. In the days when I did a lot of lung and liver biopsies, I would tell the patients the potential complications are A, B, C . . . "and rarely, death." Think of it this way. Suppose every time someone got in the car with you, you had to go over every potential complication or possibility of injury or death. No matter how many times you have been down the road, no matter how safely you drive or how carefully you obey all traffic laws, you know as we all do, that sometimes "blank" happens. We don't usually think about it in these terms, but anytime you get into a car, there is a statistical chance you will be accidentally killed. Think about the relative safety of someone riding in the car with you and then think about what the statistic for accidental gun death vs accidental motor vehicle death would look like.
Doctors, like motorists, have somewhere to go, and almost always a good reason to go there with the procedure they perform, and usually take all reasonable precautions. But there aren't any guarantees of an accident-free environment, in medicine, on the highway, or anywhere in any aspect of your life.
Be careful out there. Shoot safely. Follow the rules. Thank the Lord for watching over you and those you love, ever day of your life.