Triple meta_key on custom SELECT query

Your Query is incorrect. To retrive meta values for triple meta_key you will need 3 different joins using posts meta on posts table.
Check code below:

// Example value
$user_id = 1;

// Calculate average post rating for user
$ratings_query = $wpdb->get_results(
                     $wpdb->prepare("
SELECT pmeta.meta_value  
    FROM wp_posts
      LEFT JOIN $wpdb->postmeta AS pmeta 
        ON (pmeta.post_id = $wpdb->posts.id) 
      LEFT JOIN $wpdb->postmeta AS pmeta1 
        ON (pmeta1.post_id = $wpdb->posts.id) 
      LEFT JOIN $wpdb->postmeta AS pmeta2 
        ON (pmeta2.post_id = $wpdb->posts.id) 
    WHERE $wpdb->posts.post_author = %d AND 
    $wpdb->posts.post_type="post" AND 
    $wpdb->posts.post_status="publish"
      AND (
        pmeta.meta_key = 'rating' 
        AND CAST(pmeta.meta_value AS CHAR) != '0'
      ) 
      AND (
        pmeta1.meta_key = 'anonymous' 
        AND CAST(pmeta1.meta_value AS CHAR) != 'true'
      ) 
      AND (
        pmeta2.meta_key = 'original_author' 
        AND CAST(pmeta2.meta_value AS CHAR) = ''
      )", $user_id), ARRAY_N);

To retrive meta data using custom query, you will need 1 joins for each meta data pairs on posts table as above.

if you print last SQL query using code echo $wpdb->last_query; , you will get SQL query:

SELECT 
  pmeta.meta_value 
FROM
  wp_posts 
  LEFT JOIN wp_postmeta AS pmeta 
    ON (pmeta.post_id = wp_posts.id) 
  LEFT JOIN wp_postmeta AS pmeta1 
    ON (pmeta1.post_id = wp_posts.id) 
  LEFT JOIN wp_postmeta AS pmeta2 
    ON (pmeta2.post_id = wp_posts.id) 
WHERE wp_posts.post_author = 1 
  AND wp_posts.post_type="post" 
  AND wp_posts.post_status="publish" 
  AND (
    pmeta.meta_key = 'rating' 
    AND CAST(pmeta.meta_value AS CHAR) != '0'
  ) 
  AND (
    pmeta1.meta_key = 'anonymous' 
    AND CAST(pmeta1.meta_value AS CHAR) != 'true'
  ) 
  AND (
    pmeta2.meta_key = 'original_author' 
    AND CAST(pmeta2.meta_value AS CHAR) = ''
  )