I reckon this kind of thing happens right across the range of professions. I am constantly irritated by people making ill-conceived judgements about scientific stuff; GM foods, biowarfare, MMR etc, where people with a basic grounding in science would tell what was tosh from what is reasonable. Unfortunately, most people in the media don't have a clue, so never pick up on the fallacies and errors that get propagated this way. Just like in court, there is often no-one who can pick up on inadequate knowledge or understanding.
Dr Meadow qualifies for annoying bloke in my book, beacuse as well as not understanding stats, he also clearly hasn't got a clue about genetics. It is likely that the cot death kids in the cases described all had genetic (and probably also environmental) factors that predisposed them to cot death.
And right across bioscience, statistics is a woefully under-taught (and in my case ill understood) part of data analysis.