The get-better-anyway effect is too vague. Say theory A predicts value x is in the range [3.1,3.3] and you observe x=3.36 +/-.1. Also, there is a theory B that predicts x>0. Theory A has been much more severely tested so is supported by the evidence. Theory B, meh.
I don't understand how more studies testing theory A and getting 25%, while excluding theory B from testing, can show that A should be preferred over B. The rationale that A has been tested more thoroughly and therefore has a smaller confidence interval sounds circular.
That is not a theory. You have to come up with an explanation (a theory) for why it should be that value. Then from that theory you deduce predictions for what it should be under other circumstances. If the predictions are consistently close to the observations it indicates you are onto something.
I expect it to be much easier to come up with a statistical prediction for the get-better-anyway effect (regression to the mean), with more specificity than x>0. It would be needed regardless, in order to exclude the null hypothesis.
There is no reason to ignore RCT results, but that is not the only way to get the necessary data (which is what I disagreed with). An RCT is also not sufficient on its own, you need the theory that explains the results as well.
Perhaps when you say in the first post "give people placebo", you mean "give the placebo to some subset of the individuals leaving the remainder untreated"? I agree that you can often draw useful conclusions from an observational study as long as some comparable individuals receive each treatment, and as long as you can control for the initial differences between the treated and untreated. But if you are saying that you don't need to look at the results for the untreated group at all, then I think you are mistaken.
I meant just placebo. I am using predictive skill of the theory behind the explanations to distinguish between them, this is common in physics/astronomy/etc. As noted by asherer, placebo effect has been studied for a long time in the manner of seeing how two groups differ. There is nothing wrong with RCTs, but does near sole reliance on them (and their observational analogue) appear to have lead to cumulative knowledge and growth of understanding?