I also have avr-1312 with apple tv and it works fine. Sometimes it blinks ond at the begginging when I select DVD (I use it in the DVD input) but it stops after 2 or 3 blinks. These blinks happens more whith my PS3, but also only just after selecting GAME (Sometimes it only stops when I touch hdmi cable and connections). What happens sometimes with my apple tv is that I can see the menu and apps, but it does not load the images, for instance movies covers), then I go to config and push to restart and it works. For sure you have already tried but what comes to my mind is connecting apple direct to your tv and also via denon with another tv to try to find out where the problem is. I would guess it in denon's problem. I also have another problem with my denon that I do not know why subwoofer only works when signal comes in Dolby Digital (then Dolby Digital becomes one of the sourround sound options and works grear), but if signal does not come as dolby digital, the best sourround sound I am able to select is DTS NEO, and subwoofer does not work in this option. Some channels as discovery channel comes with dolby, but others like history channel don't. Regards.
I have the same dang issue with 4th gen. I've tried multiple cables. For some reason avr1300 flashes and Samsung tv says no signal. Have you been able to figure this out?
Horrible. I'll make a few suggestions. Try 50 herts which i saw you didnt , switch apple tv and lcd 720p both. Try different lcd, led tv. If you think its the connection and tried other cables already, try different outputs from the avr. The hdmi output can be 4k and its trying to upscale, maybe the regular 1080p will do. Good luck.
I had the same issue with my Denon E 300. Folks at Denon told me it's an HDMI handshake issue and can be fixed with reverse HDMI handshake procedure. But it didn't work for me. So I just exchanged it for another one from best buy.