Comment 3 for bug 269109

The fix is to give www-data ownership (owner+group) of the folders.

Forgive my shorthand of not specifying the group, its implied...
$ man chown
    chown [OPTION]... [OWNER][:[GROUP]] FILE...
    If a colon but no group name follows the user name, that user is
    made the owner of the files and the group of the files is changed to
    that user's login group.

It might of been clearer if I had explicitly specified the group ownership, such as:
    - chown www-data:www-data /var/lib/joomla15/tmp
    - chown www-data:www-data /usr/share/joomla15/modules
    - chown www-data:www-data /usr/share/joomla15/templates
    - chown www-data:www-data /usr/share/joomla15/plugins
    - chown www-data:www-data /usr/share/joomla15/language