I'm not going to say that the original studies are correct, but this is a fallacious analysis as well. You can't use broad, population-based observations (which are subject to countless possible confounding factors) to dismiss a targeted study that attempts to isolate a single cause and effect relationship.

Suppose a large portion of schizophrenia cases are caused by toxo. We know the toxo infection rate differs massively between countries, but the schizophrenia rate is consistent. Therefore, there must be another cause of schizophrenia such that its prevalence as a cause of schizophrenia is almost perfectly anti-correlated with toxo infections. More toxo infections, less of this other cause. Or there could be a correlated factor that prevents schizophrenia. Maybe having a cat, in and of itself, prevents schizophrenia.

That seems extremely improbable, considering that a priori we should think that a particular amoeba causes schizophrenia is not probable.