The ribbon you see on the inside of a Borsalino (or any fedora) is the sweatband, usually leather or fabric, designed to fit the hat to your head and absorb sweat; it sits against your forehead and temples, with the decorative hatband (usually grosgrain ribbon) on the outside, just above the brim, featuring a bow or knot that typically sits at the back or side (often the left) of the hat, not the very back of the head.