Steven Novella has thought a lot about thinking. I offer in evidence the following post from his Neurologica blog: The Context of Anecdotes and Anomalies.
The problem with anecdotes is that they are subject to a host of biases, such as confirmation bias. They are easily cherry picked, even unintentionally, and therefore can be used to support just about any position. For every anecdote, there is an equal and opposite anecdote.
I really liked it, and heartily recommend the whole thing to the friendly local conspiracy theorists. Unfortunately, I also predict that they will fail to recognize it as a valid indictment of their epistemological shortcomings. Oh, well.