At least the way I've heard it, the doctor problem is given as an answer to the question "Why don't we test everyone for HIV/cancer/horrible disease X?" See for example the discussions people had when the American Cancer Society recommended that women with average cancer risk delay their first mammogram to age 45.
It's relevant to that question, but it's also cited regularly as an example of how "even doctors can't do stats".
Which, like most people, they probably can't. But asking someone with lots of experience with a situation, a question about a superficially, but not actually, similar situation adds another level of confusion beyond inability to work out the numbers logically.
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