Perhaps the pax arrived at the bag drop quite late and the staff thought it'll be better to speed up things by taking the bags in and trust the granny to do the payment prior to the flight. If time was an issue here, perhaps sending the pax to pay first and then return to the bag drop would have been too late for them to be accepted.
After the bags have been taken in, one of two likely thought patterns may have taken place:
1) The granny has gone to pay but been unsuccessful. Because the time was already short, she decided it'll better to board the plane and deal with the payment later (and then "forgot"). Perhaps, if she's both unfamiliar with airports, flying and how it all works, she was also overwhelmed and felt clueless.
2) The granny saw the bags being accepted and quietly decided 'stuff it, they are in without needing to pay anything, not going to spend good money now...'.
Either way, they fell foul when JQ cross-checked the data and discovered the luggage was over limit (compared to what had been purchased).
I'd make a guess that JT may also be a very infrequent flyer. Otherwise he would have made sure to explain to the granny what to do at the airport. FWIW, I've taken people to the airport and accompanied them through the check-in / bag drop until they disappear into the security queue. Sometimes I've taken them to the gate (domestic) and waited there until the plane has departed, just to make sure everything goes well and they get to depart (
tactic best suited with MIL's though not personally tested... ).