I’m convinced that the genetic effects that provide us with extreme visualization and problem solving skills are related to this particular failure mode, where schizophrenia is also common in the family tree.
Saying this as someone whose mother scored in the top 1% on the SAT and was schizophrenic.
Schizophrenia is different that it is at least partially behavioral. The brain is more like an adaptive neural network, so it's sometimes hard (or impossible) to disentangle hardware from "behavioral configuration". In the case of schizophrenia I think (not a doctor!) there is a (perhaps structural) disposition toward modes of thinking, psychosis, delusion etc. -- thought and behavioral patterns that develop if there is inadequate self-assessment in place (which is how I would explain identical twins differentially developing the condition), and experiences of stress and trauma that can disrupt benign thought.
It is a terrible condition... I have close family members with psychosis too (that's somewhere in the spectrum of bipolar to schizophrenia). For me it appears quite clear why intelligence has a protective effect (and one of the many reasons I value, and cherish, intellectual activities of all kinds so much).
Counter to opinions elsewhere (where you shouldn't live in the "shadow of the disease" through genetic screening, family history, etc.), I personally do think it's important to be mindful of it. That way at least symptoms may be recognized early and treatment can be more effective (since it is at least partially treatable and has a large behavioral aspect). Here's hoping we never develop it.