Well, I think that really depends on how we actually operationalize what "free will" is.
But, on the topic of therapy, I think the point of this article is that CBT (or DBT, or whichever drug is the one of "choice") are touted as being the "evidence based" solution, where "depth psychology" or psychoanalysis are reviled as unscientific and ineffective.
What the article seems to trying to point out is that the only reason one could make that case is because of bias in research methods and results reporting. So, are CBT or psychotropic drugs really more effective that psychoanalysis? I don't think there is a universal answer to that. Insurance companies want to push drugs or CBT, because they have a vested interest in making the case that it delivers results "faster." But, as you point out, the reality is, it likely is not faster at all. And maybe not even more effective.
But, we tend to just have an empirical bias, of sorts, maybe born out of a sort of notional sciencism. Sure science works, empiricism works, but that doesn't mean it works best for everything.