Bottom line is (1) without the flight coupon, an airline cannot get the airline that issued the ticket to pay for the flight but (2) all airlines do have a procedure in place for lost tickets and refunds.

In this instance, the agent did what he/she was supposed to do and there really was little choice, even if the thing is kind of harsh on the kid.

Which BTW is one reason why I like e-tickets. (The other one being that with e-tickets, you don't depend upon having to receive a paper ticket, and having to send it back if changes are needed. So I can get the airline to issue it directly, and change it over the phone in the worst case.)