Statistics by definition lose information, and part of understanding if you’ve lost the “right” information is to look at the individual cases that are excluded

Statistics by definition lose information, and part of understanding if you’ve lost the “right” information is to look at the individual cases that are excluded by the model. So yes, in those cases the anecdotes do trump the “science”, if by “science” you mean a lossy, probably-biased model of the real world. What you can’t do with anecdotes is generalize them to the entire population, but taking an honest look at them is an excellent way to find methodological gaps.