alt Hacker News19 subjects, assigned sedentary or active based on habitual physical activity levels. Subjects were screened on basic health measures.
The problem with this is that people are sedentary or active for a variety of health-related reasons that are not captured in any screen (esp. the crude one used in this study). As a predictive study, this is fine, sedentarism predicts a lot of bad things. But it doesn't, on its own, suggest that becoming active is helpful. See also grip strength and mortality.
The principle of what you're stating is true, it could be correlational.
But there's an enormous volume of evidence that exercise, especially intense exercise, is better for health than any other intervention, including more sleep, quality of diet, pills+supplements (except those that treat an active illness/disease of course).
There's even compelling data showing that moderate drinkers who exercise live longer than non-drinkers who don't exercise. Even given that Alcohol is a powerful carcinogen.
The only thing proven more effective than exercise is weight loss really, if starting from high bodyfat levels.
(Anything above ~15% bodyfat in men seems to have negative implications for lifespan, and ~30% for women)