There's an interesting story of a Japanese family driving in the early hours of the morning on the first day of their trip to America. The police thought the car was weaving erratically and tried to pull it over going full lights and sirens.
Unfortunately in Japan all police cars go with lights at all times and if they want you to pull over they not only put the sirens on but also shout an instruction over the cars megaphone system. So the driver, a Japanese lady in her early forties ignored them and sped up thinking she was in the way. Many miles later she's out of the car at gunpoint with her seven year old son in the back terrified.
This one ended happily when the police realised she was confused and didn't speak English, contacted an interpreter and helped to her a motel for the night. If you want a really weird story though, look up the Japanese lady who went in search of the bag of money buried under the snow by Steve Buscemi in the movie Fargo. Even though people tried to explain it was just a movie she continued on her quest eventually, and sadly, succumbing to exposure.