Someone drops dead right after eating a strange fruit. Maybe they had heart disease and coincidentally died right after eating said fruit, but it's far more likely that the fruit had something to do with it. This is a perfectly statistically valid assumption, given that the vast majority of plants are toxic.
Once you live in a bayesian universe, every anecdote is data. Every data point might be incorrect; that's a given. The "plural of anecdote" line is just a particularly rigid way of frequentist thinking.