Change conditional tag in wordpress without editing the core files

Question

In wp-admin/includes/class-wp-posts-list-table.php lines 59-69:

if ( !current_user_can( $post_type_object->cap->edit_others_posts ) ) {
            $exclude_states = get_post_stati( array( 'show_in_admin_all_list' => false ) );
            $this->user_posts_count = $wpdb->get_var( $wpdb->prepare( "
                SELECT COUNT( 1 ) FROM $wpdb->posts
                WHERE post_type = %s AND post_status NOT IN ( '" . implode( "','", $exclude_states ) . "' )
                AND post_author = %d
            ", $post_type, get_current_user_id() ) );

            if ( $this->user_posts_count && empty( $_REQUEST['post_status'] ) && empty( $_REQUEST['all_posts'] ) && empty( $_REQUEST['author'] ) && empty( $_REQUEST['show_sticky'] ) )
                $_GET['author'] = get_current_user_id();
        }

The code above controls the display of 'Mine' tab in the post edit screen (which appears beside: All, Published, Drafts, Pending.. etc):

Apparently, this only show up to users who can't edit_others_posts (Authors and Contributors for example).

Can I change this condition so that 'Mine' tab would show up for all users? Without hacking this code file.