There may be circumstances where you may want to watch a rented movie on your iOS device where you have no Wi-Fi or 3G connection (e.g. on a flight). Apple’s official documents state “an Internet connection to the iTunes Store is required to authorize playback.” So, the question is whether an internet connection is required to watch a rented movie?
Answer is simple. The authorization takes place when you download the movie. Watching the movie does not require an internet connection.