You can read an example (http://science.sciencemag.org/content/351/6277/1037.2.long, http://www.be-md.ncbi.nlm.nih.gov/pubmed/26941311/#comments) I linked in another comment (https://news.ycombinator.com/item?id=11325254). There are quite a few blogpost on this also, and if you allow me to shorten the story in one sentence, that is a comment on Science arguing a previous study on Science did the statistical analysis wrong is under the critics that the comment itself did statistical analysis wrong.
And recently life sciences fields are in a "reproducibility" controversy which basically arises from education and application of the topic.
The first time I got a biostats lecture in medical school, I genuinely questioned their advice. By the third class, I was convinced I knew nothing about math. Luckily our biochem prof was a physics major and assured me I didn't need to worry about the stats.
Somewhere in residency, I realized I really had been getting all the stats questions right. But not because I did anything like the other residents. They have all these crazy stories and mnemonics to keep track of what kind of problem they're looking at. They seriously try to classify their way out of basic math. They classify. Everything.
I now agree with my profs. I didn't need a stats class. But the stats education in medical school seems designed to convince physicians that they need statisticians. Which is probably a coup for biostatisticians, but it's a damn shame for physicians trying to break into research outside major academic centers.
Relevant to your main point - I have worked with many clinicians. Most of them have had a fairly tenuous grasp of the statistics they were working with, which matches your experience in training I think. A couple had much better understanding, but had driven that education themselves.
It is true that depending on how statistical mechanics is taught, it can be difficult to connect to other statistical reasoning (the distributions are "nice", you have a gazillion measurements, and your population sampling doesn't tend to have bias issues, etc.)
I've had to do a lot of extracurricular statistics to get up to speed but a disturbingly large portion of people don't. People generally know t-tests and maybe ANOVA, and that's about it. Of course they don't know any of the theory behind it and often just apply t-tests to everything, even when inappropriate.
How can you possibly say that? Are you familiar with the course prerequisites for every biology and medicine degree in the world off the top of your head?
And quite frankly, the PPV trope is just that, a trope. The biostatisticians found a little trick to lord over their masters. If you only have 15 seconds to solve after reading the question, and you know you only do this once every 6 months, and you know most people get it wrong, answer C, next question.
Christ, the story that docs suck at stats is part of medical education. They don't teach biostatistics, they teach "you suck at biostats".