Hi Darrin,
Please remove the old code and use this. It shows for both the displayed user as well as the directory item.

/**
 * Get an array of member type labels based on member types.
 *
 * @param array $member_types member types.
 *
 * @return array
 */
function buddydev_get_member_type_labels( $member_types ) {

	$labels = array();
	if ( ! $member_types ) {
		return $labels;
	}
	foreach ( $member_types as $member_type ) {
		$mtype_object = bp_get_member_type_object( $member_type );
		if ( ! $mtype_object ) {
			continue;
		}

		$labels[] = $mtype_object->labels['singular_name'];
	}

	return $labels;
}

/**
 * Print the list of member types of the user in member directory.
 */
function buddydev_show_member_type_labels() {
	$user_id = bp_get_member_user_id();

	if ( ! $user_id ) {
		return;// It should never happen but in case someone put the ac
	}

	$labels = buddydev_get_member_type_labels( bp_get_member_type( $user_id, false ) );

	echo join( ', ', $labels );
}

add_action( 'bp_directory_members_item', 'buddydev_show_member_type_labels' );

function buddydev_show_member_type_for_displayed_user() {
	if ( ! bp_is_user() ) {
		return; // just a safeguard, it should never happen.
	}

	$user_id = bp_displayed_user_id();
	$labels  = buddydev_get_member_type_labels( bp_get_member_type( $user_id, false ) );

	echo join( ', ', $labels );
}

add_action( 'bp_member_header_actions', 'buddydev_show_member_type_for_displayed_user' );

Hope that helps.
Brajesh