Anecdotal evidence has been shown to have a greater influence on opinion than it logically deserves, most visibly when the anecdote conflicts with the reader’s opinion and when the reader is not highly analytical, even if the anecdotes are accompanying statistical evidence. Though the anecdotes may not totally sway you, they can easily leave you with the sense that the research findings aren’t as conclusive as they claim to be.

It doesn't follow from this that one should downvote contrarian anecdotes. There is the obvious alternative of de-biasing the readers (e.g., through comments, PMs, posts) and oneself. This is, of course, a monumental and difficult task, but author does not mention any alternatives, which makes one question how much he has considered before settling on his solution.

(Full-texts of linked papers: [1], [2])