well, to the credit of Bayes, dementia is likely a safe choice (depending on age/etc.) but dementia is largely a diagnosis of exclusion and most doctors, besides being unfamiliar with Bayes, are also just plain lazy and/or dumb and shouldn't immediately jump to the most likely explanation when it's one with the worst prognosis and fewest treatments...

I work in biomed. Every textbook on epidemiology or medical statistics that I've picked up has had a section on Bayes, so I'm not inclined to believe this.

Here is research about doctors interpreting test results. It seems to favor GP's view that many doctors struggle to weigh test specificity and sensitivity vs disease base rate.

https://bmjopen.bmj.com/content/bmjopen/5/7/e008155.full.pdf