What I meant is that you can't say with absolute confidence that supplementing for vitamins cured his migraine without accounting for the placebo effect in that experiment.
It's not a valid experiment regardless. There are too many confounding factors and too small a group.
It doesn't matter. Medicine is a lot less about proper science than we'd like to believe. It's about helping people feel better. Science is a crucial tool for that, but it doesn't always work, while random guessing sometimes does. Even the science is often supplemented with random guessing.
Eventually, you take enough random-guesses-that-worked and apply science to it. That gives you a lot more confidence to recommend it to other people. But often, confidence is all you get, rarely certainty.
Yeah, you're definitely right; I should have added in the end "among many other factors".
While I admit that n is pretty small indeed and thus doesn't qualify for a proper and rigorous clinical experiment, the reason I mentioned the placebo effect in particular is because of the fact that some symptoms or diseases have some psychosomatic streak to them, if you will, and therefore the role of the placebo effect in these cases becomes more pronounced to research and investigate but if the OP felt way better after the treatment, that's what it all counts like you said.
It was no nitpicking or mischief on my part raising this issue :)