Beecher concluded that, overall, in 35 percent of cases the condition was "satisfactorily relieved by a placebo," which he took to be evidence of therapeutic effectiveness.
It wasn't my field, but I figured the folks in the field had vetted it and it could be relied on--though I wondered about placebo in animals.
There turn out to be some issues with the study, and with others following it. One obvious problem is that there's no control to study placebos. You can treat a patient, fake-treat a patient, or not treat a patient. The author calls for such studies. One of these things is not like the other things--and a lack of treatment is not exactly comforting. (Comforting can be a big deal in helping. Feeling like you've been rejected may cause problems.)
Plus, a lot of people just get better with or without treatment. The body is designed to try to repair itself, and often it succeeds.
There are fluctuations in severity of a disease or of pain. If you have a threshold (the patient has to be worse than X to start my study), there's a chance that there'll be a fluctuation below the threshold later--briefly feeling better. Or briefly feeling worse--some studies didn't take "getting worse" into account properly.
I'll not say there's no such thing as a placebo effect (and the author is careful not to say that either), but the situation is certainly much fuzzier than popularly believed.