It wasn't clear in the article whether the family made it explicitly clear to the airport agent that the lone passenger on the ticket was a child. Even if they did make it clear, I doubt the agent could make the change without involving ticketing. After the 24 hours grace period, any changes to the PNR, aside from special meals or seat selection, requires re-issuance of the ticket. That includes changing the ticket from an adult to a minor (and then the family's PNR must be linked to the child's PNR). I just tried to book a dummy domestic ticket for a child, and AC.com doesn't even allow me to do so. It has a warning message that a child must be travelling with an adult (defined as 16 years or older), and that to make such a booking one must contact AC reservations at least 48 hours prior to scheduled departure. So within the OLCI window, it's already too late.

Granted, not every family has a SE member in the household that knows the rules reasonably well; however, it doesn't take away the need to know some basics to avoid such incidents. How to book tickets when travelling with children is one of them IMO.