I have the same problem. Also have a Samsung TV (1080p) and non-4k 4th gen AppleTV. Trying to play a movie rented from Apple movies plays a few seconds of video then the video goes black and I only hear audio. If I try to fast forward the video and play it will give me an error saying I do not have an HDCP compliant cable. I've tried many different cables and all show the same results.
I tried resetting the AppleTV, TV and receiver to defaults still no luck. I connected the AppleTV directly to my TV and still same behavior.
My TV is not HDCP compatible at all and the manual for my receiver says this about HDCP:
When the connected equipment is not compatible with copyright protection technology (HDCP), the image and/or the sound from the HDMI TV OUT jack may be distorted or may be lost.
This is exactly what I'm experiencing. My 3rd gen Apple TV can play the same video without issue, but this runs a much older version of software that I'm sure never implemented HDCP.
I watched a movie via Apple movies the other night with this exact same setup and everything worked fine. The title I'm trying to watch tonight happens to be available in 4K where the other was not.
So my theory is that Apple has implemented HDCP support on 4K media streams without validating that there is end to end support for HDCP available and/or validating HDMI is even running at 4K resolution. Sloppy.