Cannot project my Macbook air AppleTV movies on a projector

Is it possible to project an Apple TV movie via HDMI cable to a projector? In my experience recently the answer is no. The HDMI cable is successfully mirroring my MacBook Air screen to the projector right up to the point where I push play on an Apple TV movie, and then the screen goes black. The audio of the movie still plays through the projector but no movie, new or old in Apple TV will play through the projector. This point to a copyright problem that Apple does not want any of their movies projected ever from a MacBook or an iPhone to a projector. Please help me find a solution to watch my Apple TV movies on my projector.