LabCorp made (income) $600 million last year. Quest made $1.5 billion.
They can afford teams of very capable developers. They can have the best software, the best presentation, slick mobile apps, speedy information systems.
They don't not because they can't afford it, but because they don't want to afford it. As is the case with many of these companies that get disrupted by tech startups, they see it as a cost center and minimize it.
Software rules the world. Any business that doesn't adapt to this will see strange little upstarts steal all of their thunder.
Regarding your point on Bayes Theorem, that's valid in some ways and invalid in some ways. Suppose someone gets a vitamin D test back at 8 ng/mL. There's not really a chance of a false positive. He's deficient and needs supplementation. Making the test cheaper, faster, and more accessible can really only improve the health of the population. It will likely also drive down the cost of healthcare overall, because vitamin D deficiency has all sorts of unpleasant effects.
Furthermore, the literature suggests that the vast majority of doctors do not understand Bayes Theorem. Source: http://yudkowsky.net/rational/bayes
Meanwhile, if I suspect that, for example, that my BMI veers into the obesity range when my TSH is high, it should be perfectly fine for me to try and get a $50 test to examine if there's a correlation. Better than spending that on a DVD of Keeping Up With the Kardashians, don't you think? Might even increase awareness about general health in the US.