I'm not the best to answer this because I don't know every application but there is something called HDHomeRun that I think may do what you want? I got an android box to ditch the traditional cable way of watching TV. Instead I mostly use Hulu / Netflix and more "on demand" viewing.

Short answer is, no androidtv device can play or record TV straight out of the box.

you need to have a server (hdhomerun or a computer with a USB TV tuner and software like tvheadend) that will communicate to androidtv through an app.

I hoped it would be great for my parents, but in the end it's just as complicated for them as the current TV setup