When you add video to a video editing project, it becomes a part of that project. It takes on the properties of the project you've added it to. Which, in the case of 4K, means that when you add your 4K video to a project set up for 3840x2160, the video is effectively 3840x2160.
In any video editing project in any program, you are not editing the original video. The video is being added as a source file of the video editing project. The only 4K project settings available in Premiere Elements is 3840x2160.
You can make and custom 4K ( 4096x2160) export but Elements does not let you make a 4K project.
It does not go any higher then UHD (3840x2160) which everyone calls 4K but actually is not.
That´s means I cannot, with PE 15, use my DSLR camera fully strength since the highest resolution I can get in PE 15 is 4k UHD. In order to save a project or export a project with high resolution such as 4k DCI [4096x2160], then you have to use Premiere Pro or what until Adobe releases a new version of Premiere Elements that includes higher resolution then 3840x2160. Have I understood it correct?
If you double 1920x1080 each direction you get 3840x2160 and is correct 16:9 aspect.
So I see nothing bad about that called 4k for short.
There are both full hd 1920 wide, and 2k wide as well, but not as common for real.
Monitors are usually either 1920x1080 or UHD often called 4k - what about UHD monitors, are they 4096 wide, or 3840 wide?
And to complicate things even more - there are such things as rectangular pixels - like for HD is 1440x1080 where width is stretched over to 1920 at presentation.
So don't feel PRE is inferior, I would not....
So if your video import is 4096x2160 but the max setting is AVCHD / QFHD 16X9 then surely you will have errors when trying to add 'Shake Reduction' as the project sizes will not match?