When a user uploads an image to the "assets" folder they can not remove the image or see it at all in the "Files & Images" section of the site.
If you are in the editor and hit the image button, the side contentpanel with the Form_EditorToolbarImageForm is loaded. This panel should ether default to "Uploades" and not allow upload to the "assets" folder or the "Files & Images" tab should show the root folder.