Hmmm considering I don't wash my hair prior to or during an event, although I have been known to end up under water now and then during, casn't say I have ever worn my hat with clean hair, BUT granted tis not like not washing one's hair for weeks on end...
as to the sig picture, my hair hadn't been cleaned in three days...
the problem being, we can think up tons of great reasons for using them, but evidence so far, doesn't support the common use of them by sailors from the GAoP as head coverings, the one picture William Red Wake originally found, so far, unfortunately is about the only one ever posted in Twill that could possibly be a sailor... although I sure would like to find more...