What are the exact hypotheses? It is difficult to say anything so generally. If the hypothesis is that there is a correlation between having X and feeling Y, once you find the correlation, you are done. If you want to test whether people feel Y only because they believe that X causes Y and for no other reason, you have to find somebody who doesn't believe that X causes Y. I can hardly imagine a situation where it is impossible, but if it is really impossible, the hypotheses

1. People with X feel Y because they expect to feel Y when having X
2. People with X feel Y for some other unspecified reason

may as well be experimentally indistinguishable. One can do better if the second hypothesis is more specific, or if the mechanism of placebo is better understood. But, as I have said, you should give an example where you can't find few people who don't share the placebo-causing belief.