Scientists' use of statistics is often problematic, but that doesn't mean that its valid to counter statistics with anecdote unless you have some larger argument.
Right. But it is also not valid to bring up statistics unless you can properly qualify their relevance, which is almost never the case. This requirement sets much higher bar for anecdotes than published statistics, when the latter rarely deserves that high bar.
As a result, most arguments about science are invalid from a scientific-method point of view. But the claims brought up -- including anecdotes -- are often interesting and informative.
