It sounds to me like they had a reservation but the ticket was never issued. The key question is whether there ever was a ticket receipt showing a ticket number, not just some confirmation number. If they had tried to do OLCI (ideally well before going to the airport) but weren't able to get boarding passes, this should be a red flag that someone needed to call AmEx travel and/or the airline ASAP.

BTW, what part of AmEx Travel was used? I've never had such a long wait to reach PTS by phone and the agents usually seem very competent.