I've just implemented the technique described at http://wordpress.org/support/topic/wp_nav_menu-list-only-2nd-level-separate-submenu/page/2 when implementing a theme for a client. When I run the theme locally on my WordPress stack it behaves as expected displaying only the children of the parent menu item. When I deploy this to the server it displays all menu items including parents and children which obviously isn't the desired result.
functions.php: http://pastebin.com/vSnEqzED
template header: http://pastebin.com/5TS4aP6K
generated source: http://pastebin.com/W7ZezJFG
Any ideas?