A basic statistical fact is that correlation doesn't equal causation. Any student of basis statistics can tell you that.
So let's assume the survey and study was done without any biases and produced a strong correlation between a State being religious and high use of anti-depressants and medications, still it won't prove anything.
A comprehensive study would have to take consideration of many other factors that separates the "religious" states and "non-religious" states. And as we can imagine, there would be many confounding factors to affect the accuracy of such a study.
So strictly from a statistical point of view, we can't conclude much from the limited information provided in the article. That's just my take on Statistics, being an AP Stat teacher.