Version 3.13.3 (not reflected in the Version select widget in the Bug tracker)
Using KDE Development Platform 4.13.3  I believe KFileSave is the name of the component that saves files.

Make it so that I can edit LocalSettings, and the webserver can read the file
chown greg:www-data /var/www/core/LocalSettings.php
chmod 640 !$
-rw-r----- 1 greg www-data 5501 Sep 29 10:50 /var/www/core/LocalSettings.php

Edit with Kate
(Kate changes the group to 'greg', and now the Mediawiki web app is broken because Apache can't read the file)

ll /var/www/core/LocalSettings.php 
-rw-r----- 1 greg greg 5501 Sep 29 10:50 /var/www/core/LocalSettings.php

==Workaround==
Launch Kate with sudo, and it doesn't change ownership of the file.  This is a risky and poor workaround because this also means you don't have all your personal settings in Kate, and you might not even be able to launch it with sudo over an SSH session to a remote host (without X-forwarding for root).