There seems to exist a lot of misconceptions about the PS4 Pro in regards to whether it supports "true" 4k resolution or not. I think Sony is to blame for not making it clear in their promotional material.
You see, there seems to be this really prevalent notion that the PS4 Pro does not support rendering to 4k (ie. 3840x2160 pixels) at all. That it instead always renders to some lower resolution (like 1440p) and upscales it for the 4k display.
This misconception is so prevalent that when I have corrected it eg. in some YouTube comments, people have directly told me that I'm wrong, that the PS4 Pro does not support 4k resolution rendering and it will always upscale.
But that's not true. It is true (and probably the cause of confusion) that the PS4 Pro will render existing PS4 games at a lower resolution and upscale them, by default. However, new and patched games can, if they so wish, support native 4k directly, with no upscaling. In other words, they will render at exactly 3840x2160 pixels.
There are already examples of exactly this. Two of them are The Last of Us and The Witness. Both support two modes of rendering: 1440p upscaled to 4k at 60 frames per second, and native 4k (ie. 2160p) at 30 frames per second.
Sure, if you want these games to render at native 4k, they will only run at 30 FPS, so you'll have to make a choice between resolution and framerate. However, they do have support for native 4k rendering, with no upscaling.
These misconceptions seem to be all over the place, and not only among the general public, but even among people who should know best. For example a representative for Microsoft (promoting the upcoming "project Scorpio" console) derided at some point the PS4 Pro for not supporting "true" 4k. Even though it does. (Ironically, the idea was that Microsoft's upcoming would support it... yet it has turned out that it actually isn't significantly more powerful than the PS4 Pro, and won't support "true" 4k any significantly better. Probably at about equal level.)