Plus the study includes “schizoaffective disorders”...the schizophrenia designation came after mathematically hacking, chopping, and filtering the data from all of those low power studies you aptly pointed out.
If they are sure of their conclusion, they themselves should design a high powered prospective survey to prove it, and pay with their own funds or funds from people who volunteer the money.
Absolutely they should design a prospective study. But I don't think they would pay for it themselves or get money from volunteers for it. In all of my career, I have almost never seen research done with private funding. It's always government funding.