Yeah, I'm very well aware how double blind works and my point is exactly related to your 2nd paragraph. Be it coincidence or actual real placebo caused healing (which happens) it would be a major perspective trauma and it definitely happens!
Personally I do think that mental states absolutely impact biology through many invisible forces like hormone production and behavior. So getting a placebo and believing that it works can stimulate specific hormone production or healthy behaviors like going for a jog which ends up legit healing the person. It's easy to see how this could lead someone to a more spiritual or religious point of view because in this experience something like "faith" is legitimately healing them tho not in the way they think.
I think it's moot to discuss this without bringing up the actual law cases and I'm not going to lie - I'm a bit too lazy and this is too depressing for me to sacrifice my time for.
My faith in US' justice system is not great though so you might very well be right.