Different methods of therapy appear to be equally effective despite having theoretical foundations which are conflicting with each other. The common aspect between different therapies seems to be "having someone to talk to", so I'm inclined to believe that really is what's behind the success.
Other kinds of conditions, like depression and anxiety, respond to a wider range of therapy styles. But those aren't the only conditions that people seek to treat through talk therapy. (And it's also an exaggeration to say that just having any conversation will help to treat anxiety and reopression. But it is probably true that treatment of these conditions is less technical and responds to a much wider range of styles.)