I meant placebo as baseline effect (from all sources, psychosomatic or statistical), and the falsifiable prediction is it should drastically decrease in situations where regression to the mean should not happen.

I think the core point of that article (and one I agree with) is that if we want to attribute the 'placebo effect' to medical care, we need to measure not the difference between the patient before and after placebo treatment, but the difference between the after for no treatment and the after for placebo treatment. And so it seems very useful (for determining the social benefit of medicine / homeopathy / etc.) to separate out psychosomatic effects (which are worth paying for) from statistical effects (which aren't worth paying for).