They did however:
> Body mass index adjustment modestly attenuated associations for several cancers, but 10 of 13 inverse associations remained statistically significant after this adjustment.
So even for two thin people, exercise seems to have helped. I legitimately don't see how you could design a study that you'd be satisfied with.
Adjusting for BMI does not solve the problem, because there are many things besides BMI (unmeasured confounders) which affect both cancer risk and willingness to exercise.
it's the same with red meat causes cancer studies. they say they remove smoking and lack of exercise and still wave the statistical significance.
it's very questionable how they removed the influence of these variables, since meat eaters do smoke way more, and do not exercise, and care about their health less.
I would have been happy if the authors just tried to factor in other characteristics like socioeconomic status, education level, etc. It looks like they didn't do that but instead just observed an "association" which isn't terribly interesting or informative.
The problem is the press representation of the papers as something they're not.
These types of papers should be published, because they are necessary to decide which hypotheses to test with interventional studies.
(Edit: I just re-watched his segment. He does talk about P-hacking and perverse incentives, which is at least a reasonable-size chunk of the problem, just not the failure mode for this particular study.)
The problem is that people's willingness to exercise depends on their health as much as or more than their health is affected by exercise. Because this study did not involve an intervention (it just pooled a bunch of surveys), it can't distinguish between exercise causing reduced cancer risk, or a third variable affecting both.