How does a study like this control for the fact that if you are depressed, you might not want to exercise that day? And thus it’s mental health that drives how much you exercise, not the other way around?
In that sense, if feeling too depressed for extreme sport, maybe a walk ever now and then should at least not be neglected.
So, one option is to ignore depression and look at other things.
They did not establish causality in the study and they also said that inactivity might be a symptom of poor mental health. The people who had less mental health days might not be physically ill, but rather, socially ill. If you read the full study and some of the interesting demographics you will see what I mean.
It really tells us nothing but puts more stigma on people who are ill making it seem like it is their fault they are sick.