by Ken Task.
course backup area is in the 'sea' of files /moodledata/filedir/
user private area is also in the 'sea' of files, but supposedly seen only by user that made the backup.
So if teacher makes a backup, it goes to private area and admin user can find it only by making query of DB mdl_files table. If admin visits course, restore, then may not see the backups made by the teacher.
There is a plugin that helps ... All Backups
get the version that is compat with your version of Moodle core.
'SoS', Ken