My guess it is #2 as well, alas.

When I was in college I wore a particularly large Tom Mix with what was known as a Montana Roll. This thing was Big, WITH A 91/2" brim.

To make a long story short I spent about six weeks with a headgear arrange met on that precluded wearing a hat. I vanished into the woodwork, no one knew where "the Cowboy with the Hat" went. To make matters more absurd, I still was carrying my knapsack that has a bear bell on it. People hear the tinkle of the bell and would look around expecting to see "the Cowboy with the Hat" and look right past me, shake their heads and pay no attention to me.