Maybe it would help if I posted the rumour.
"Sony’s (SNY) plan to introduce an 80-inch XBR LED television set with 4K resolution is said to be the start of a larger scheme to push 4K on consumers, much like 3D was a huge push in the industry a couple of years ago. Since 3D isn’t gaining much traction, Sony (and we’d assume the rest of the industry) is betting on 4K as a way to get consumers to upgrade their home entertainment devices. Sony is already selling 4K Blu-ray players for $200, and the company’s next-generation PlayStation 4 will indeed support 4K resolution playback as well, a source tells us. Like the PlayStation 3 did with Blu-ray, Sony is betting that by including the ability to support 4K resolution media — games and movies — consumers will have an incentive to upgrade to new 4K television sets'"
The keyword there is playback, there is nothing to suggest that games will be in 4K hence no one is suggesting that games will be native 4K, hence no one is argueing they can't. Well I guess some people in this thread are suggesting they can't but then again no one is suggesting that it will.
The PS4 offering 4K movie playback tho is a given, Sony already sell 4K Blu-Ray players, why wouldn't they support 4K on the PS4? The real question is if they will include a scaler to upscale PS4 games to 4K.