If you made the change to the sudoers, it should work. Open a console, and try:
su - www-data
sudo -u root find "/home/public/data/music" -maxdepth 1 -not -name '*.id3'
The last one is the command who retrieve the files from disk, and if it ask for password, you must allow that "find" command to be run using sudo without asking for password.