Tuaw.com reports that the developers of the WALTR video upload app made the discovery while testing their app. Unfortunately you can't transfer 4K files using iTunes, so you'll have to use an alternative service to get them on your phone, but once there they seemingly play without a hitch.
Of course the quality will be limited by the resolution of the screen, so the larger and higher resolution iPhone 6 Plus is a better bet for viewing them than the iPhone 6.
Given the hoops you have to jump through and the fact that the iPhone 6 can't shoot 4K video this obviously isn't a big feature for Apple, or not yet anyway, but we've heard reports that the iPhone 7 will be getting a huge camera boost, which may allow it to shoot 4K video.
Then of course there's the iMac with Retina 5K which recently arrived, so it's clear that Apple has its eye on higher resolutions. Plus since the A8 clearly supports 4K video it's always possible that Apple will add the feature to a new version of Apple TV.
We're not optimistic that Apple will bring official 4K support to the iPhone 6 though, or not until an iPhone which can also shoot 4K arrives anyway, but it's nice to know the feature is there in some capacity.