Hi Rodger,
It does for live TV but not ondemand, the 360 ' knows ' you only have a HD TV so will not allow to watch a UHD source such from ondemand. The best example is the Virgin UHD channel you can watch live streams but not ondemand, unless there has been a change since I last checked on my mini box and HD TV.
Edited to say you might be better asking whoever is writing the software for the 360 I can only say what happens not the why.
Also can't say what happens with a 4K app as I haven't tried, but assume it would be the same if played through the 360.