items_wrap not working

your problem is in your use 'menu_class' and 'items_wrap' not synchronized.

You can edit :

wp_nav_menu( array(
                'theme_location' => 'header-menu',
                'container' => '',
                'echo' => '0',
                'menu_class' => 'nav-menu horiz-menu container sixteen columns',
                'items_wrap' => '<ul class="%2$s">%3$s</ul>'
            ) )

or:

wp_nav_menu( array(
                'theme_location' => 'header-menu',
                'container' => '',
                'echo' => '0',
                'items_wrap' => '<ul class="nav-menu horiz-menu container sixteen columns">%3$s</ul>'
            ) )

Apologize for my English is bad !