Yes. And the researchers know that too. There's an entire section of the paper devoted to teasing this apart. From the third paragraph of the paper ("Methods")

Yes. And the researchers know that too. There's an entire section of the paper devoted to teasing this apart. From the third paragraph of the paper ("Methods") "[T]here are multiple threats to the validity of such an approach. We were particularly concerned about factors affecting a young person's probability of attending Scouts–Guides, which could also be protective of mental health in later life. To test for this possibility, we used three approaches. First, we explored a form of ‘negative control’ exposure. Specifically, we investigated whether attendance at other types of organisations (voluntary groups and the church), and other outside school clubs, which might have a similar set of common factors encouraging attendance and which might be protective of mental health in later life, were also associated with better later life mental health, conditioning on scouts–guides attendance. The absence of an association would suggest that an unmeasured common factor was not confounding the scout–guide association, while the existence of an association would be ambiguous with an unmeasured common factor and a third factor, independent of scout–guide attendance, but acting in a pathway through the other types of organisation on mental health, being possible. Second, we sought evidence of a dose–response relationship, exploring whether fractions of attendance were related to better mental health. Third, we explored whether the Scout–Guide association was weaker in regions with a higher proportional attendance which might suggest Scout–Guides not being the causative agent."