Schizophrenia is, to my understanding, sort of a catch-all phrase for several different problems with similar symptoms but different effective treatments. Even in the study, they found only 49% of people with schizophrenia were infected.
It's really weird to characterize diseases by their effects rather than their cause, because then you don't really have a disease per se, but rather a pattern of symptoms that may or may not always have the same cause.
One major example is SIDS (Sudden Infant Death Syndrome), which appears to be little more than a medical term for "the baby died of asphyxiation and we can't figure out how".
That's also synonymous with "it's a viral infection".
The depressing part is that such umbrella terms prevent study of the causes, because they likely come from many sources, and muddle any research.