I'm not aware of any research that says a placebo won't help a "non-believer" - can you cite a study? Given the study I linked where they were deliberately handed inert pills and told that they were an inert placebo, and they still worked, I actually strongly doubt your claim.
And given the research I linked, why in the world wouldn't you believe in them? They do rationally work.
A single study is not sufficient grounds to believe in something, especially a proposition as complicated as "placebos work" (it may not sound complicated expressed in this way, but if you taboo the words 'placebo' and 'work' you'll see that there is a lot of machinery in there).
See previous discussion here and note my remarks, I recommend reading the linked articles.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
If continuing the discussion becomes impractical, that means you win at open threads; a celebratory top-level post on the topic is traditional.