Apple promotes the rental service as being able to allow viewers to watch, start/stop, content on all account related iOS devices.
It would be nice but I've never seen them explicitly advertise that.
- If you download a rented movie on your computer: You can transfer it to a device such as your Apple TV (1st generation), iPhone, iPad, or iPod if it’s a standard-definition film (movies in HD can only be watched on your computer, iPad, iPhone 4 or later, iPod touch (4th generation or later), or Apple TV). Once you move the movie from your computer to a device, the movie will disappear from your computer's iTunes library. You can move the movie between devices as many times as you wish during the rental period, but the movie can only exist on one device at a time.
- If you download a rented movie on your iPhone 4 or later, iPad, iPod touch (4th generation or later), or Apple TV: It is not transferable to any other device or computer.
I know I've seen the start/stop language in Apple's promotional material for movies. But perhaps I'm confusing it with references to movies "purchased" as opposed to "rented". I was using iPad because it's much more efficient to browse and search Movies and Trailors- but prefer watching content via AppleTV. You're correct that I can probably stream it to AppleTV using AirPlay.
It's rare that I ever rent movies from iTunes and so I'm a bit surprised. Netflix and Hulu+ are seamless where platform issues are concerned. Never a problem continuing a movie reserved via iPad or web, on iPhone, AppleTV, and/or desktop computer.
Thanks so much. Now I can stop moping around and staring at the TV screen, waiting for my movie to show up.