Heavy Wool Winter

My friend just started dating this girl he met at the beach. She's got some weird habits that have started to concern him though. She was wearing a hat, that he thought was for the sun, but she wouldn't remove it. When it started raining, then she took it off. When the sun came back and got really hot, she went to her car and put on a heavy winter coat lined with - get this - "Platypus wool". He though she was just a little odd, but they went skiing and she wore shorts and a tank top in the Rockies.
Also, she likes to bike, and he thought she was healthy because she rides her bike everywhere, but it turns out, she only rides it for distances of a mile or more. If it's around the block, she drives her car, even to go thirty feet in the city, she insists on using the car.
She also told him she doesn't believe in airplanes and refuses to go to an airport to see proof.
Is she joking, trying to make him go crazy, or is she a loon herself?