It seems that in restore_ui_components.php in the function search(), the process by which the backup/restore/import area creates the list of available courses is to grab 250 courses from the database and test them 1 by 1 to see if the user has the correct capabilities to proceed. Unfortunately, if their courses don't get grabbed in that 250, it still returns "No courses available". The SQL that gets the list of courses does not pair down the list, so the SQL is incorrect and the process is poorly designed.