My uninformed guess is that they mean that a statistical AI system might come to similar conclusions as humans such as concluding that there exist thunder gods, while a non statistical type (one with just "reason") would not come to that conclusion about thunder gods, and as such would not as accurately model humans.

Simple models of correlation and causation often make bizarre predictions, like the famous conclusion that pirates cause global warming. A statistical learning system cannot step outside its own predictions to fix such problems.