"PlayStation 4 Pro made its big debut yesterday, and Sony is selling it as a 4K gaming box. But most of the games the company showed were not rendering a native 4K image. Instead, you were probably seeing something closer to 1440p or 1800p. That’s quite a lot less detail than 2160p — although, for the Sony’s new supersystem, it doesn’t matter.
The PS4 Pro does not have the horsepower to render native 4K. Developers are already admitting that. Guerrilla Games confirmed that it isn’t rendering Horizon: Zero Dawn, its open-world sci-fi adventure, at the 3,840 x 2160 resolution that is standard for 4K. Sony itself plainly stated yesterday during its event in Manhattan that it didn’t want to make a machine that could fill all 8 million pixels of a 4K television set."
Mark Cerny: Brute-force rendering techniques can of course be used to support 4K displays, but they have unfortunate consequences for console cost and form factor.”
http://venturebeat.com/2016/09/08/ps4-pro-isnt-4k-that-doesnt-matter/
To put it simple, Sony has found a way to achieve 4K without the need of brute force or a significantly more powerful system, if you will. So unless you plan on sticking a magnifying glass up to the screen, you are not going to know the difference. Anyone else without their knowledge would have to render that screen native for the same results leaving fewer resources to be used elsewhere.
These guys are not a hardware company for nothing.
Its not TRUE 4K though