Originally Posted by Often1

Arguing with a law violator is pointless and a waste of your time.

1. Tickets containing flights to or from the US are covered by US law (DOT rules).
2. Tickets containing flights departing the EU are covered by EU law (EC 261/2004).

Both require a full refund to the original form of payment, neither are based on the passenger's citizenship or residence, and neither is premised on "transit". For what it is worth, the US has not, since 1999, had or recognized transit and thus NZ is doubly wrong.

In the case of US flights, file a DOT complaint (online and free). Also, in both instances, initiate a chargeback with your credit card issuer (bank). Be succinct and document everything. Provide a copy of your e-ticket receipt, the notice or other proof of cancellation, your request for a cancellation and either the denial or the absence of communication. Keep copies and screenshots of everything. When you submit your complaints and chargebacks, focus on the requirements of the law, e.g., that the flight was cancelled and that the ticket is covered.