“While the longitudinal associations in our study are compelling, the design of the study did not allow us to demonstrate a cause-and-effect relationship,” Braley explained. “Additional prospective work that includes information on strength of the human-animal bond and its effect on cognitive trajectories, and incorporates study of biological mechanisms that could mediate this relationship, are still needed.” (Braley is Tiffany J. Braley--one of the authors.)

This can be an interesting finding and a prompt for further research, but I absolutely agree with a caution about turning correlation into causation. The burden of proof should be on the affirmative.

Also, it's difficult to have a well-informed debate because the link is to an article about the paper--not the paper itself.