SELECT 
  CASE
    WHEN record.is_public = 'Yes' THEN 'public'
    WHEN EXISTS ( SELECT 1
      FROM permissions
      WHERE permissions.rec_id = record.id AND user_id = $user_id )
      THEN 'accessible'
  ELSE
    'private'
  END
  AS viewable,
 record.id,
 record.display_name
FROM
record
WHERE 
record.id = $rec_id; # or other criteria