Remember, association does not mean causation. We have to make sure the confounding variable ( teenagers who excercise more are outside and teenagers who sit and play video games are more likely to be inside) is not artificially slewing this association.
However, I believe it plays a role. A very good prospective study ( unlike this study) in Finland showed giving huge doses of vitamin d to infants prevented Type I diabetes in the future by a significant amount and followed them for 30 years.
Needless to say, I gave my daughter this dose of vitamin d from day one 9 yrs ago before the APA increased its requirements for children and infants.Thirty years later, participants were surveyed to determine whether they had developed type I diabetes. The results of the study showed that infants who were given 2,000 IU or more of supplemental vitamin D per day had an 80% lower risk of developing type I diabetes, compared with infants who were given less than that amount