Under what conditions is internet required to watch a rented/downloaded movie on iPhone/iPad?
You always need an internet connection to start the rental period in my experience. Only a few packets need to transfer from the device to the server - so you are not streaming the movie.

Think of it like a credit card authorization - without the central server "charging" the rental, the 24 hour playback window can't start properly.

Your experiment that some rentals play is interesting and hopefully someone has a deeper packet analysis to present, but the safe bet is to not rely on a rental if you don't have in-flight WiFi to start the rental period and authorize the movies you intend to have "activated for watching" during the flight.