After a hat is removed from one's head, hair will relax, take in moisture from the air, and in a short while show little or no evidence that a hat was worn. I have heard, anecdotally, that baby powder can be sprinkled into one's hair after hat removal and when combed out, voila, hat hair is gone. (I have not tried this first-hand.)
Perhaps (I don't know for a fact though) a good 19th Century/early 20th Century barber took into consideration where on a head a hat would lay and cut a client's hair with the lessening of "hat hair" as an objective.
When one considers the small negative effect of hat hair against the positives of protection against sun-related skin problems, keeping dry in the rain, keeping warmer in the cold, a nappy fashion statement, a new image and the like -- hat hair is no concern at all.
[Late note, added May, 2007] Hat hair is not necessarily a negative. The April PEOPLE'S MAGAZINE included a note entitled HAT HEAD IS HOT in their "World's Most Beautiful People" feature. Actor Eric Bana is quoted as saying "I look my best when I take my helmet off after a long motorcycle ride. I have a glow and a bit of helmet hair."