This is all wrong. 1080p scales perfectly to 4k. If anything, it looks smoother due to more pixels. Anything between 1080p and 4k will look better on a 4k screen, because you know, the 1080p screen doesn't have enough pixels to output that information.
That's in theory.
In practice, playing 1080p games (PC/PS4) on my Samsung 40JU7000 (that is considered to have a good scaler) didn't look anything like playing on a 1080p native TV.
You could clearly see the effects of upscaling.
It didn't look horrible either and I was also using it as a PC monitor so I was pretty close to it, but still pretty disappointed as I expected more.