(I should pause here and note the danger of confirming nontestable theories though, as Karl Popper once wrote, "Once, in 1919, I reported to him a case which to me did not seem particularly Adlerian, but which he found no difficulty in analyzing in terms of his theory of inferiority feelings, Although he had not even seen the child. Slightly shocked, I asked him how he could be so sure. "Because of my thousandfold experience," he replied; whereupon I could not help saying: "And with this new case, I suppose, your experience has become thousand-and-one-fold."" http://www.stephenjaygould.org/ctrl/popper_falsification.htm...)
Go back and look at all the arguments the doctor makes. Once you remove the vague handwaving, you're still left with the basic question: what are you measuring, analyzing and deciding? Can computer aided methods do it better and more accurately, and in the areas they can't, why not, exactly? - and can this be improved? If so, it's a matter of time.
I am not saying a computer can replace a nurse's bedside manner or a doctor's ability to make the final call but computer aided medicine would seem to be as superior to regular medicine as computer aided chessplaying has long been shown to be superior to both grandmasters and computers alone.
Even the maxim he quoted, that doctors should only measure things that may affect the diagnosis or treatment, is a heiristic not unlike the chess heuristics that guide grandmasters' thinking. But how often does a tactical line or particular "hidden" property of a position override that heuristic? And similarly, a computer can help uncover hidden correlations that a simple human rule may miss. After all, medicine thought for millennia that washing hands was just a ritual with no medical benefit until bacteria were discovered.