Truth Be Told: Nice Story, but still does not reflect the beliefs of the Rov. The mere fact that a person always wore a hat the rav felt he should wear one even if it is hot. If you asked the Rov if a YU boy should wear a hat, I am 100% sure his answer would be different.
Rabbi Aaron Rakeffet, who studied under the Rov himself said :To me it’s a compliment that I don’t need [a black hat] to be frum…..because being a Torah Jew is the most important thing in the world.” Did he have anything against it? NO, but wearing a black hat does not make a good Jew.