What they are actually doing is refusing to _pay_ for a lab test (they don't want to support paying for it or billing anyone else for it). They can't refuse to examine the results if you pay "cash" and have the copy sent to them. So if you really want to address something with a test, then first you can insist that you want a test done on your own dime (and you unravel the nightmare of dealing with insurance on the phone), or you can insist they give you the name of a lab which you can use to get the test done yourself and then you do that legwork. They might insist that the test results might take too long and you need antibiotics right away (both which may or may not be true) yet you can also tell them you're refusing their treatment because they don't have enough information to make a fully informed diagnosis and walk out.
I view the current situation of antagonistic-doctors as ridiculous, because if a consumer is willing to pay, then they should be offered the resources to do so, which increases the specificity of their own treatment, and doctors shouldn't stand in the way; yet they do, and thus prevent consumers from acting in their own best interests.
If you really want to see a doctor stammer platitudes about their choice of treatment, state that you require them to check your genomic sequence data for statistical likelihoods before they make a proper diagnosis.