Problem:
Once you get everything setup and your permissions right, users are still not able to see comments or updates that have been posted to the ticket.
 Solution:
The solution I found on Drupal's forums. I am merely posting here for my own sanity because I know I will be looking for this later and not be able to find the thread. Link to solution thread. Number 11's solution works!
Line 2354 of the support.module file (found in sites/all/modules/support) has this:
<?php
            global $user;
            $ticket_alias = $query->leftJoin('support_ticket', 'st', 'st.nid = ' . $nalias . '.nid');
              $query->condition(db_or()
                ->condition(db_and()
                // Must be on the allowed clients list