Question for Katia

So, Ash and I were watching the episode of Monty Python's Flying Circus that includes Mosquito Hunters this weekend, and now we have a question for Katia or any other Aussie who wanders in.

The intrepid hunters are shown wearing a hat with one side of the brim rolled up, sort of like this, or like this. Why is only one side of the brim rolled up? Was there a reason why people did (or do) wear a hat like this? We hypothesized that it might be because it would be easier to shoot a gun or a bow and arrow, but then it seems that a similar style would have evolved in the United States, especially in the West. Yet this style of hat is something that we (and obviously also the British audiences Python was originally intended for) identify as "Australian"-- though I suspect it's about as Australian as Lederhosen are German.

I tried Googling, but didn't come up with anything helpful. I know you pop in here every once in a while, so I thought I'd ask you directly. What's the story with the hats?