Sorry - my response was deleted or blocked or something. You can search for Blackmagic Ultrastudio Recorder 3G. My link was not allowed, probably. I got mine on eBay, otherwise looks like the price went up retail to $140.
The Blackmagic app that gets downloaded is really more for capture and editing rather than viewing, although you can watch in the capture window.
Watching a DVD is basically opening a file. There are protocols for watching a DVD. Copy protection is built into DVD watching that satisfies the industry. Streaming video real time from an outside source is not done the same way a local file is transferred and simultaneously played back. There’s other protocols and industry permissions standards put in place.
I’m actually thinking of getting an ATV just for watching live TV on one of my
monitors. Going through all the gymnastics of streaming to a computer and the work around isn’t worth it, but I do prefer the remote over dealing with a bunch of apps on my Mac. Too much effort to find and download them, plus the ATV UI mirrors my other ATVs. I get what you’re doing and the frustration of unsatisfying answers is understandable. It just feels logical, but the industry has conspired to not make it allowable