This was a cross-sectional study. Here's an opposing result for anxiety and depression: > Testing Causality in the Association Between Regular Exercise and Symptoms of Anxiety and Depression > Context: In the population at large, regular exercise is associated with reduced anxious and depressive symptoms. Results of experimental studies in clinical populations suggest a causal effect of exercise on anxiety and depres…
The thing is, since a few we actually know now how exercise helps: it builds resilience against depression[0][1]. The press release from the Karolinska Instituted website[2] explains it fairly well, but in short: when you're stressed, you produce kynurenine. How kynurenine works precisely is unknown, but what is clear is that having chronically elevated levels of it can induce all kinds of mental illnesses. Skeletal…
Both papers you cite are by the same group, and I don't think the results represent a consensus of the experts.