I agree, it would be nice if there was some kind of token handoff between web browser and app - and this would be the ideal way of handling it. I really, really dislike webviews in iOS apps because they're almost always clearly a webview - but they don't usually have all the same functionality.
So, that's one way they could easily overcome these limitations on the TV. See also: Existing Apple TV's approach to sign in, requiring users to use a computer or web browser to visit a page protected by OAuth and then type in a code from their TV to pass the session on to the TV. Or YouTube's even other approach of YouTube TV involving, IIRC, typing codes into your console/TV box from your YouTube website.