I have been having the exact same problem, and I am outside of the United States but my iTunes account is from the United States.
I have never had problems streaming purchased movies, shows, or music before.
Now I can see all that has been purchased and even select them. However, when a movie or show is played, it shows the spinning wheel for a couple seconds and reverts back to the movie/show details screen. When music is attempted to be played, a "content not found" error occurs when a song is selected.
Interestingly, movie previews can still be watched just fine.
Also, if I restore or reset the Apple TV I can immediately watch one move or show video, but the second time this is attempted it reverts back to the original error.
This means that I have to spend 4 minutes resetting the Apple TV just to watch something.
Apple support was not able to resolve this.
Netflix and other apps work just fine.