On many fedoras, both modern and vintage, you will find that the liner has a plastic shield at the top, which is meant to keep the liner free of sweat and oils from the top your head.
That being said, apart from my top hat, all of my hats touch the top of my head, and I don't mind it.
That being said, apart from my top hat, all of my hats touch the top of my head, and I don't mind it.