I am not really sure how theaters really get the rights or what determines things like distance. Well, I know a little I guess from talking to people that run theater companies, but not the technical terms or anything. So sorry if I am not phrasing this correctly...
I know that there are different things that go in to it. When you buy the rights you can just buy the general rights that allow you to perform a show. However, there rae more extensive rights (from what I understand) that you can but that would cancel out any contracts to put on the show within a certain mile radius. This happened to a friend of mine who runs a theater. He had bought the rights to a show that would have been a regional premier and got right up to a few weeks before it opened and another theater bought this type of rights and they were no longer able to perform the show.
I am pretty sure that the national tour has this kind of rights, that no other theaters can run Annie within a certain mile radius. But, please don't take my absolute word for that. The reason I think that is because last year there was some discussion about other theaters having to cancel thier production becausethe tour was coming too close.
Also, my daughter was in a local production of Annie this past Christmas. They did auditions last September and we found out at the cast party in December that they almost didn't get the rights because the show was coming nearby (2 hours away). The rights were not aquired until AFTER the auditions and the show was already cast. They even had a back-up show in place, just in case.