At present, you require a person with server access to create a File system repository. It is a simple process, of creating a folder. (See http://docs.moodle.org/en/File_system_repository_configuration)
Once the repository is created, only a person with server access can upload files (unless they set up FTP access for others)
1. Enable the creation of File system repositories inside Moodle by Moodle admin.
2. Once File system repositories are created, enable users at teachers level to upload files.
I've thought a bit and set this as a Major priority. Change it if you like.