I wish I had an explanation for you David. The only HDMI troubleshooting technique available to users without specialized test equipment is to substitute one component for another, since HDMI either works, or not.
There isn't anything special about the AppleTV's HDMI implementation that I am aware of, and it sounds as though you already tried other inputs on the Denon.
The only relevant Apple Support document only mentions obvious problems that probably aren't worth your time to read: Apple TV (2nd and 3rd generation): Troubleshooting video issues
All I can suggest is to have Apple evaluate it. Make an appointment:
You could also try searching for this problem on the AVS forum. Try to ignore the knuckle-dragging Apple haters.
It wouldn't be the first time I heard of a complaint regarding Denon. Unfortunately the perfect AVR does not exist, and Denon's are better than most.
I wish Apple would make one
You know it! The market is screaming for an Apple AVR. Nothing but digital inputs, configure everything using an app. Jony Ive could design it in an afternoon. Put the Beats hardware team on it.
Unfortunately it's a very small market. But it's a fragmented one, and everyone's offerings suçk in too many ways to count.
Good AVRs command a premium which would fit right into Apple's business model... anyway, enough dreaming.