I should have seen the core problem coming (your documentation is clear enough): when I perform backup with "Backup from parent directory" ON, it fails with an error message:

    * warning: chdir(): No such file or directory (errno 2) in /home/content/a/n/s/answerjam/html/test/sites/all/modules/backup/functions.inc.php on line 345.
    * backup_files(): Unable to chdir() back into directory ''

This happens in economy goDaddy Linux hosting, so I am not surprised.

However, the backup file is still created (20 bytes long), and that, probably, should not happen - a non-computer-savvy user may choose to ignore the error on the basis of "the file is there, so it's Ok".

I am filing this as a minor UI issue.