From the abstract: "Conclusions: For early adulthood, findings did not support commonplace or expert opinion that exercise behavior has a favorable influence o

From the abstract: "Conclusions: For early adulthood, findings did not support commonplace or expert opinion that exercise behavior has a favorable influence on sleep. Rather, the findings lend support to the importance of cognitive processes in the onset and maintenance of sleep complaints." They are claiming precisely what you suggest they should. Saying that the evidence does not support physical exercise having an impact on sleep is not the same thing as claiming to have evidence that exercise does not impact sleep. They simply mean that the data they collected does now show any such link. In this case, it is clearly because the cognitive processes appeared to dominate the results. To test the former directly, I suppose one would need some physical measure of good sleep. Perhaps by monitoring brain activity and restlessness.