There's always the possibility that because she's so established, Avex allows her to go outside of Japan more to film. The anonymity is a good reason for her to film elsewhere but I mean, you can still film in Japan and not be bothered if you close down a street, etc.

It doesn't matter where you are, if you have a camera crew, people are going to look because they think you're famous. For example, filming in NYC doesn't necessarily mean a crowd will be smaller. Because of the number of tourists year round, they gather regardless of whether or not you're famous.