Errors When Removing Custom Header Support

I’m trying to remove the custom-header support for Twenty Twelve.

I first tried this:
remove_action( 'after_setup_theme', 'twentytwelve_custom_header_setup', 11 );

That resulted in nothing.

Next I tried this:

function nws_theme_tweaks() {
	remove_theme_support( 'custom-header' );
}
add_action( 'after_setup_theme', 'nws_theme_tweaks', 11 );

That worked but then resulted in this error (with WP_Debug = TRUE):

Notice: Undefined index: custom_image_header in \wp-includes\theme.php on line 1452

Warning: Cannot modify header information – headers already sent by (output started at \wp-includes\theme.php:1452) in \wp-includes\option.php on line 563

Warning: Cannot modify header information – headers already sent by (output started at \wp-includes\theme.php:1452) in \wp-includes\option.php on line 564

Am I missing something or is this a bug?