Recording Apple TV (and other HDMI devices) to a HD PVR

Hello guys..

First, my setup - I have Directv DVR, Apple TV, and a PS4 - all video and audio running through my Pioneer 1021 Receiver - with a single HDMI out of my receiver right to my TV.

My question is pretty basic. I pretty much want to record PS4 content, DVR content and Apple TV content to my Mac to later transfer to an external hard drive. I am not looking to record purchased content - but actually looking to record gameplay on my PS4 - and record some streaming shows on the Apple TV (the WWE Network specifically) - so not sure if I will run into a HDCP issue or not.

So with that said - my issue is how to do this. I was looking at the Hauppague HD PVR Plus - because it has an HDMI in and out. Would that work for my needs? Could I just take the HDMI out of my receiver and run that to the HDMI in of the PVR, and the out of the PVR right to my TV? Would that work? Am I missing something important here? It seems it would be that easy - but just looking to make sure. I really didn't want to use a computer at all - I was hoping to just transfer it right to a external drive rather than using the Mac as the middle man, but I assume something like that just doesn't exist.

I do pay for a subscription - but the content on there is mostly free stuff from their shows on network free TV.

I guess I just thought it would work coming out of the receiver, because I've heard of a instances where people say that the receivers (and some HDMI splitters) remove the HDCP.