Nonsense and here's 3 definitions (from 3 separate online dictionaries) that say so:
Hat: a shaped covering for the head worn for warmth, as a fashion item, or as part of a uniform.Hat: a covering for the head, especially one with a shaped crown and brim.
Hat: a head covering which is worn for various reasons, including protection against weather conditions, ceremonial reasons such as university graduation, religious reasons, safety, or as a fashion accessory
No nonsense at all. I read all three paragraphs. Nowhere did it mention or describe a baseball type cap. It described various styles of HATS. Another pet peeve is the lazy, or careless reference to T-shirts. Back in 1947 when that style came on the scene, they were Tee Shirts; alluding to golfing.