How can I prevent the post_modified column in wp_posts from being updated?

Add the following to functions.php when you are meddling and remove it after, or comment it out:

function no_mod_wpse_136092($data,$postarr){
  if (empty($postarr['ID'])) return $data;
  $old = get_post($postarr['ID']);
  if (!empty($old)) {
    $data['post_modified'] = $old->post_modified;
    $data['post_modified_gmt'] = $old->post_modified_gmt;
  }
  return $data;
}
add_action('wp_insert_post_data','no_mod_wpse_136092',10,2);