I'm not a researcher, but it seems your logic goes the other way, too: if you walk and your health improves, then there seems to be a positive correlation between health and walking.
And, I think we can control for the health decline. I.e., Stopping exercise because you have cancer vs. stopping because you have broken leg. And even then you can control for changing up the type of exercise. My wife broke her foot last year, and shifted from running 20 miles a week to doing "sit and bit fit" exercise. She actually improved her cardio capacity.
Finally, I think the logical conclusion of your argument is: exercise has no impact (or maybe even a negative impact) on health. Studies and every day experience don't seem to bear this out.
And, I think we can control for the health decline. I.e., Stopping exercise because you have cancer vs. stopping because you have broken leg. And even then you can control for changing up the type of exercise. My wife broke her foot last year, and shifted from running 20 miles a week to doing "sit and bit fit" exercise. She actually improved her cardio capacity.
Finally, I think the logical conclusion of your argument is: exercise has no impact (or maybe even a negative impact) on health. Studies and every day experience don't seem to bear this out.