Duke has affiliation is with the Methodists. So is Americans. And American leans liberal.
All rankings - no matter the ranker - is based on whatever methodology they use.
You missed the point. I was providing the OP a list of schools that have cognitive science - but i was letting them know this isn’t a cognitive science rank, so the top ranked school may not be strong in cognitive science. That list will give them schools that have a program that they can go further research.