As I have written previously, there is a lot of confusion out there about whether the PlayStation 4 Pro supports running games at native 4k resolution (ie. 3840x2160 pixels), or whether it always renders games at a lower resolution and upscales for the 4k display. I think that much of the blame on this confusion can be put on Sony, who haven't made it clear enough in their promotional material.
The answer is, of course, that yes, the PS4 Pro can render games at native 4k, without upscaling. This, however, is a choice made by the games (or, more precisely, the game developers) themselves. Games can choose the resolution at which they will be rendered on the PS4 Pro, and 3840x2160 is a perfectly valid option, and there are already several games with this support.
The confusion probably stems from the largely advertised property of the PS4 Pro that it will render existing games (ie. those made for the base PS4 model before the Pro was published, and which have not been patched with higher resolution support) at a lower resolution, and upscale the result for the 4k display. This has given many people the wrong impression that it will do the same with all games, even new ones, no matter what.
The misconception is, somehow, really prevalent, and can go all the way up to people who really should know better, such as video game reviewers, and gaming company representatives. Also, some PC gamers who are eager to deride and attack consoles and their users, fully embrace the misconception to make fun of the PS4 Pro and claim that it's not "really 4k". It's actually quite egregious the extents they will often go to make that claim.
In an online conversation I corrected someone's direct claim that the console can't run games at native 4k. Regardless of my correction, he insisted for several messages that I was the one who's wrong, and that the PS4 Pro will always render games at a lower resolution and upscale. It took several posts with links to articles and pictures to convince him that it does support native 4k without upscaling.
But, of course, rather than admitting his error and his misconception, he then started moving the goalposts, and coming up with other requirements for a system to be "true 4k".
The first one that everybody always presents is, of course, that it can't run those games at 60 frames per second when in 4k resolution. As if that were somehow a requirement for something to be "true 4k". I have never heard of such a requirement anywhere. It's a completely made-up one.
But even that claim is false. There's nothing stopping the console from running a game at native 4k resolution at 60 FPS. The choice is made by the game developers: Do they prefer framerates, or graphics? The console, or Sony, is hardly to blame if game developers go for graphics rather than framerate. And, as of writing this, there is at least one game that does run at 4k@60FPS: FIFA 2017. So it's not like it's impossible.
Of course now the goalposts are moved once again and, apparently, if it can't run all games at native 4k and 60 FPS, then it's not "true 4k". Apparently, if there exists even one single game that it can't run like that, then it's not "true 4k". The requirements just keep piling up. Of course this requirement pretty much means that there exists (and will probably never exist) no platform that's "true 4k" in this sense. From the millions of games out there I'm certain you can always find at least one that the system can't run at native 4k at 60 FPS, no matter how beefy your computer may be.
It all comes down to the definition of "a 4k system". Some PC gamers are eager to pile up requirement after requirement just to make the PS4 Pro not "true 4k" (while at the same time making pretty much all PCs, no matter how powerful, likewise not "true 4k"), but that's not really a reasonable way of defining the concept.
The simplest and most reasonable definition of a 4k system is if it has support for 4k displays (ie. 3840x2160 pixel displays), and can show content using that resolution.
After all, this hasn't always been so even on the PC side. 4k support is actually surprisingly recent. For instance, the first Nvidia graphics cards that had support for 4k resolutions was the GTX 600 series, published in 2012. In fact, pretty much no computer (PC or Mac) nor console had 4k support prior to 2012 (except, possibly, some early prototypes).
If a computer (or console) supports a 4k display, and can show content using that resolution (eg. video material, or anything else), it pretty much means that it has 4k support, plain and simple. Frame rates have absolutely nothing to do with this. Graphical quality has absolutely nothing to do with this. There is no standard by which 60 FPS is somehow a requirement for something to be "true 4k". That's completely arbitrary. (And even then, as said, the PS4 Pro can run a game at that refresh rate. It's up to the game developers whether they want it or not.)
On the PC side there's all this "is your PC 4k ready?" thingie. Which is completely and absolutely arbitrary. The minimum requirements for "4k readiness" are a complete ass-pull. For example the benchmark score thresholds for a "4k PC" in benchmarking software are completely arbitrary, and constantly changing. It's up to somebody's opinion. There is no standard for this.
The 3840x2160 resolution is a completely unambiguous absolute form of measurement. Can your system output to a display of that resolution, showing content with that many pixels? If yes, then it has 4k support. Easy, simple, unambiguous.