I would speculate that when placebos appear to work, it is primarily because they don't do anything
I like your argument but, amazingly, there's some research that seems to indicate that placebos affect a physical change. In cases where heroin was used as a pain killer, a placebo could be blocked using the same chemical that blocks the effect of heroin.
Here's more: http://www.newscientist.com/article/dn7892