Apple also sells a product called an HDMI adapter. And "Display Mirroring" isn't really display mirroring if there isn't also content playback since content plays on the "display" as well. Some apps block HDMI output, however the Video app does not, therefor all videos should work.
Also if this excuse of "well you could hook it up to a giant TV and do a "public showing" violating copyright law" is valid, that means all purchased movies via iTunes would not play via HDMI w/secure HDCP link either. Except they do, and since "public showing"s of owned movies is also a violation of copyright law, by your logic all iTunes purchased movies should only play on Apple Devices and not on any TV Screen.
Additionally if your "solution" is to buy another $99 peripheral that logic is flawed as well considering I could hook up the Apple TV to ANY DISPLAY WITH AN HDMI PORT and AirPlay content to it and give a "public screening" in clear violation of copyright law, however I would have paid an additional $99 for the privilege.
Furthermore, Apple doesn't produce products that don't work. The HDMI adapter works for all apps that explicitly allow it as well as all Apple built in Applications and successfully plays back video of all Purchased iTunes movies. By your logic, any Apple Computer that has an HDMI port also shouldn't play DRM'd content on TVs, but they work as well.
Your logic fails entirely because the Apple TV does not give Apple "end to end DRM Management" because an HDMI cable is required to hook it up to the TV, and HDMI Cables have their own DRM standard (HDCP), so the Apple TV is inherently reliant on that technology. Until Apple makes an actual TV, it will not have end to end DRM management on any content played on a TV using an Apple TV with HDMI cord, iPad using HDMI Adapter, or Mac computer using it's HDMI port or DVI to HDMI adapter (depending on age of model).
Therefore this is a real problem (without air quotes) with DRM on certain titles, for me only rentals, not with the fact that I haven't bought an Apple TV.