Typically its not that they have no control, in the cases you're talking about, but the machines do have specified dose limits still. You can press the button as many times as you like, but it typically won't let you hit yourself with a gram of morphine or something. So in that case, I can see the button being an applied placebo effect.
Sometimes (I don't have a statistic) in Israel this is used for placebo effect. Patient doesn't control anything, but still might feel a relief.