HD Cable Box-to-Old Tube TV Question...

[IntelliVolume]

In our workout room (a bedroom we designated a treadmill space because we don't have kids) we have one of the older 4:3 tube TVs (a Magnavox/Phillips) that's connected to a new HD box from our service provider, which is Cox. No matter where I leave the box's output set -- 480i, 720, 1080 -- we get a picture sent to the screen with no issues, but it's weird in that all these format outputs don't change the image we're seeing at all. I would think leaving the box set to, say, 1080i would distort the image going into this old TV or yield no image at all, but that's not the case...

What SHOULD the cable output be set to for a TV such as this? I assumed 480i, but as I said, NO RESOLUTION choice makes a difference, as we get the same picture...in fact, I can even eliminate all the output choices on this Cox HD box (by switching off those "bullet points" next to each resolution output selection) and it STILL shows a picture on the TV...

Weird, indeed...

Can anyone help?