(1) Use your personal discretion. Some anecdotes are funny. Others can be perfectly cogent rebuttals, especially when people make overbroad statements.[a]
(2) The author is right in some respects: you need to be aware of the ways that stupid stories can bias you. Even being aware of this fact is sometimes not sufficient, so use downvoting to try to protect others.
(3) Lots of people believe in anecdotal responses to anecdotal original-claims. [b]
(4) A lot of people tried to be funny by offering anecdotes to be downvoted. Unfortunately, people haven't consistently taken the advice above, so they are not all in one place (at the bottom). That is a pity -- this would have been a fun and interesting use of downvotes.
[a] Actually, the discussion is full of overbroad statements of this form like "no universal truth" and someone presenting "nothing should be above questioning" as above question.
[b] I would like to formally respond that this is generally stupid -- you don't clean up a house by flinging crap at the crap. Your mileage may vary.