Apple TV app in iOS: I searched for “Total Recall”, because I wondered if I had already purchased it. Two matches. Neither was purchased. So, I never bought it then, I thought at first. But I decided to scroll through hundreds of movies that I’ve bought in iTunes, and, hey, what do you know - there it was!
Wish the library had a separate search field, or at the least, hits from the library would be included in the search.