Commonsense, like ulcers are caused by diet and anxiety, or that salt raises blood pressure?
I think a good point is made: statistical evidence is also misleading - it deliberately ignores (averages out) the extreme cases. The results are a distribution; statistics folds that into one number. Anecdotes fill out the distribution.
Ulcers are not generally caused by diet and anxiety, but rather by bacterial infection. Anecdote is a much more compelling refutation of "common sense" than it is of empirical statistical evidence.
Statistical evidence is not misleading; it's simply the case that if you are seeking outliers, as in your example, then looking at measures of central tendency won't contain what you're looking for. Anecdote has no role in "fill[ing] out the distribution."
I think a good point is made: statistical evidence is also misleading - it deliberately ignores (averages out) the extreme cases. The results are a distribution; statistics folds that into one number. Anecdotes fill out the distribution.