Derek,
In these cases, there is no place to store them as system files. The filebrowser normally (historically?) associates an uploaded file using the plugin file mechanism with a specific course and activity instance. The file is then backed up and restored along with the activity. Theme settings are not associated with activities so the file browser is not really an appropriate tool to use.
The image tool or filebrowser has been hacked to allow inserting of image urls with certain repositories instead of the actual file. For example wikimedia finds a image to download and then offers an option to put the url instead. This sequence seems a little strange to me, but works.
It might be better to have ask first whether the user wants a file or a url and pull up a browser with repositories that support that type. The url browser alone could be available in themes, etc.
Daniel