The iconography associated with the WWII sailor had some indecorous connotations I don't think in its heyday BYU would've wanted to be linked to.
I'd be surprised if it's not neo-retro. Unless something like Blue Print's explanation -- of it representing a well known part of an archaic school uniform -- is correct. I hadn't heard that before, & am skeptical.
The young WWII sailor was often in port for a very brief period, so he had no attachments to worry about when he mingled with the locals. He naturally picked up quite the reputation. Not necessarily bad by a national standard -- but definitely mirthful -- & not in a BYU sense.
mutu.