Watching 4K Content on 4K Apple TV

So here's my question... When watching 4K content on the Apple TV that you own (purchased in iTunes), can you stream it locally in 4K (from your itunes/computer on your network) or does it have to stream from Apple's iTunes servers in order to play in 4K??? When you look at the file on the computer, it shows it as a 1080p 60fps video file even though it shows as 4K HDR in the iTunes store. Take "Wonder Woman" or "Fantastic Beasts and Where to Find Them" for example. Both are 4K on the store, but show up as 1080p on your computer when you look at the file info. This makes me to believe it'll only play in 4K streaming through the iTunes servers. Is that right..?