comment_notes_before not working

As noted by @birgire, the comment_notes_before argument is only shown to users who are not logged in. If you look at the source, there is an if construct that checks if a user is logged in. If they are logged in, then a filter and an action fired. If not, then the comment_notes_before text is echoed.

If you want to show the before text to users logged in, you can use one of those hooks and echo the before content.

<?php
$before="Before";

//* Show $before only to logged in users
add_action( 'comment_form_logged_in_after', 'wpse_106269_logged_in', 10, 2 );
function wpse_106269_logged_in( $commenter, $user_identity ) {
  echo $before;
}

$args = array(
  'class_form'      => 'add_review',
  'label_submit'      => __( 'Leave a review' ),
  'comment_notes_before' => $before, //* Only shows for logged out users
  'comment_field' => 
    '<textarea id="review_text" name="comment" placeholder="Enter your review"></textarea>',
  'comment_notes_after'  => 'After',
  'logged_in_as' => ''
);
comment_form($args);