EVO has several "modes" in which you can put a NAS share. One such mode is called the "Locked" mode. When an EVO NAS share is in "Locked" mode, it will keep track of who created a file/folder, and that user will be the owner of the file/folder. When you create a folder, you own it and by default, no one else can put files into that folder.
However, you can modify the "others" permissions to allow other users to have write access. If you have write access to a directory, you can rename or move any files or folders inside of it. This is because the names of all those things are part of the directory where they are contained.
For Unix-like systems (such as Linux, on which EVO is based), a file and the file name are two separate entities. The file "name" is really just an entry in a directory that points to the file object.
So in a case where you own a folder and have given "others" permission to have write access, it is entirely possible that you own the directory but not some of the files inside it, in which case you may not be able to view the contents of a file, even though you could rename, move, or delete it, if you only own the parent directory but not the file itself.