Well, I just got off the phone with Apple Support, and apparently, the live TV integration is currently being worked out server-side. He said he was in a chat with the ATV app engineers and they said they were currently working on it. GRAIN OF SALT, etc., etc.
Odd thing was that he said it would still require the provider's app to be installed, even though you'd be able to watch content directly in the ATV app. So, I guess we'll see? (And by "we'll see" I mean, "we'll see when they update the marketing copy" lol).