Looking at the TV.
It's easy to get confused between pixels and scaling. Your TV will display at 1080i by scaling (software adjustment) even though it does not have the pixel count.
In simple terms it will display at all sorts of resolutions by software adjustment. It cannot display at 1080p because it does not have the pixels to do so or the software to handle it.
So as an example Sky TV will output at 1080i (nothing from Sky even HD is better than 1080i) and the TV will display the picture, other sources may display at different resolutions and the TV will be able to display usually 720p.