The process of diagnosing a disease works quite like scientific method. You form a hypothesis based on symptoms, and then you test your hypothesis by ordering various kinds of lab etc. tests. You inspect the results and modify your theory on what could be wrong.
The procedure you described just there is susceptible to confirmation bias. You need to take that into account, as well as the power of your tests as Bayesian evidence updates. There are a lot of doctors that order tests even though their evidential value is not high.
For example, consider a test with a 1% false positive rate, for a disease with a 0.1% incidence rate for a particular set of symptoms. If you come through positive for the test, what's the probability that you have the disease? Too many people think it's 99% (the converse of the false-positive rate); but in reality it's more like 10%. But you still formed a hypothesis, did a test, and the result came out OK. You think you're doing science, but in reality you're cargo-culting.
Double-blind trials and high-quality statistics are prerequisites for good work here.
Most doctors won't bother with ordering tests for disease with 0.1% incidence rate (or much higher) until more common and probable causes are excluded. And even then, they would most likely defer you to someone who specializes in the very narrow field who could potentially make correct diagnosis with the existing data.
Double blind trials are for clinical studies. You don't do double blind trials on single patient :D.
"Bayes Theorem, 40 year old man with microscopic blood in urine, incidence of serious illness for that symptom at that age in a non-smoker is low, so more sensible to not have the extra test. Doctor didn't understand Bayes Theorem, was deeply offended and yelled at Arnold's wife"
I chose my example to explain Bayes and the base rate fallacy nice and clearly. An example chosen on didactic grounds is easy to attack on realism grounds. But it really does happen. Honest!
My point is, if you're not accounting for bias - an easy mistake to make - you are not doing science. And thus, a doctor's diagnosis is frequently not like science, because it doesn't have good quality objective procedures to exclude it.
