Yes, that's exactly what it means. Public schools by their very nature, are immoral.
By the way, unless a man believes in God, I can't see why he should be concerned about "sin".
I don't believe in God, and I am very concerned about behavior which violates the rights of other human beings. I consider it "sin".
Thank you. On this we can agree, to some extent. If you were standing here, I'd offer my hand.