I strongly suggest you read one of Fisher's articles on the subject. Fisher did not deny that smoking contributes to lung cancer, just argued that the Hill and Doll reports failed to establish a causal link. He argued that the negative correlation between cancer and inhaling, the rate of increase in lung cancer incidence for each sex not matching the rates of smoking adoption for each sex, the high correlation with lung cancer for heavy cigarette smoking but not cigar or pipe smoking, and the correlation between lung cancer incidence and urban location all discount the hypothesis that cancer results from tobacco combustion products passing through the lungs in favor of other hypotheses. He did not claim that causality can not be established, and indeed proposed experiments to distinguish between some of the alternate explanations.

I was mostly going to say (1), but (2) certainly crossed my mind as an example of the other sort of error.