But I disagree with your counterexample - Stanford may say they do this but I don't think they do given the evidence I saw. Or at least, you'd have to explicitly seek it out as a student to get such exposure.

So we're left with your anecdotes. Lots of people have such anecdotes. People saying "I learned critical thinking at university" are a dime a dozen, but their beliefs aren't evidence they really did.

I don't think this is moving the goalposts. Obviously when I meant "no evidence" I meant no evidence that could persuade someone who didn't agree with the proposition. Just saying "yes they do" isn't evidence.