Well put, but things are actually one step beyond that. There is no reason to even bring up beliefs here for the most part, people will report things they know to be false, even without being encouraged to. There is no more common lie than "how are you?" "oh, fine", which is part of the daily routine for billions of people. Which isn't much different from saying "oh, I'm OK, I guess, not too bad". And in a clinical trial, there is a lot of influence exerted towards reporting feeling better, regardless of whether it's any true.
Those are not beliefs, they're just things people say because it's expected. And unfortunately the medical profession is very happy to exploit this, sometimes, while rejecting it at others. It's all very confused, but it doesn't have much to do with actual beliefs. People say false things all the damn time. Usually only slightly false. So very few people will report feeling 9/10 after some non-intervention, when they actually feel 2/10. But they might say "uhhh maybe 3, possibly 4, I don't know", and really the whole problem here is that it's not possible to know because there is no more right answer to "from 0/10 how are you feeling?" than it's possible to have a consensus on which flower is the prettiest, or ranking artichokes from the smoothest to the grittiest.
All of this is more than enough, when using very low standards where the smallest possible blip is somehow hailed as a miracle cure, to turn a null into a "might be of help to some". Which is another giant red flag for pseudoscience, but somehow here it all gets swept under the rug because damn would it be nice if this magical mind healing stuff was real.
There are no right answers to subjective assessments, including feelings, so it's never possible to actually check, and the statistical tools used to help are basically a joke, because they shouldn't even be used on subjective ratings anyway, even less so when any underlying answers aren't fixed. Along with massive biases in favor of non-interventions, this easily explains 90-95% of "placebo", and it's still the smallest possible effect of them all, even treatments that don't work can sometimes seem to perform better.
I have no idea how any of this debate is any different from taking a random wellness cult whose adherents swear their whole life was transformed because they bathed in some mud, or whatever. Or the healing power of prayer. It's all exactly the same thing.