It’s not just movement. Retinal tissue develops from the same embryonic tissue as the brain. They probably looked at structure, vasculature.
The best anecdote in this space- nobody with congenital blindness has developed schizophrenia.
https://www.lesswrong.com/posts/z9Syf3pGffpvHwfr4/i-m-mildly...
That is a much more risky idea in the first place, and your link provides quite a few such anecdotes.
What’s the rationale for why this might happen?
But to me, very low incidence rate for both seems like a sufficient rationale. Given that there's both viral and genetic causes for congenital blindness, it just doesn't make sense to imply the protection is genetic: even if true, there would still be cases of schizophrenia among the people that were blinded by a viral infection in-utero.