There are some authentic accounts of Bates method success stories. While there may not be many of them, and most of the ones that you have heard are probably not authentic, there is bound to be a few out there that are real. Even the weirdest things work once in a while.
There are plenty of success stories using the Bates method to restore eyesight. There are forum posts and blog entries to check when the official Bates method website seems to be too partial when it lists testimonials. If nothing else works, sometimes radical ways of doing things work. That's where something like the Bates method comes into play.
No, there are not authentic accounts of Bates method success stories, because those who have said that it works have only wished that it works. They have reviewed the stories of so-called success, and they have found those stories to be doubtful. The stories are nothing more than the placebo effect from people who want it to work.
Like so many other fads or overly hyped trends, Bates' method is little more the undocumented fiction, and has very little truth and in it. People are always coming up with new things that purport to help people do X or Y, but they are almost always false, in order to profit.
There are probably no authentic accounts of Bates method success stories. It is very hard to make eyesight better and requires laser surgery. The success stories are probably paid for because it is just another one of those things made for the creator to get rich off of. Like many things.