Private post_status in a List_Table

example.php

<?php

class Your_Media_List_Table extends WP_Media_List_Table {

/* some stuff here */

	// Adds a WHERE modify filter, calls parent version of prepare_items(), then removes filter
	function prepare_items() {
		add_filter( 'posts_where', array( &$this, 'modify_post_status_to_private' ) );

		parent::prepare_items();

		remove_filter( 'posts_where', array( &$this, 'modify_post_status_to_private' ) );
	}

	// Changes the "post_status" WHERE value from "inherit" to "private"
	function modify_post_status_to_private( $where ) {
		return str_replace( "post_status = 'inherit' ", "post_status = 'private' ", $where );
	}

/* more stuff here */

}

?>