[TeMPOraL]

You don't challenge "false, but widely held beliefs" with anecdotes - those beliefs actually is exactly what anecdote becomes when it starts being repeated.

Alerting people to new circumstances is a good use, but that's pretty much all. Proof by counterexample works well only in mathematical logic, which is not how the real world works[1]. In reality you enter the domain of probability theory, and there counterexamples work exactly as the article author says - as an evidence that needs to be properly weighted. And these are those weights that people vastly overestimate in case of anegdotes.

[1] - by this I mean, mathematical logic is not how we model, comprehend and operate reality.