Am I reading something else, or have they changed it? The linked page says:

" Emergency We’ll ensure One New Zealand customers are safe during an emergency, so anyone with an appropriate One New Zealand phone will be able to call 111 in an emergency (when voice satellite calling is available). One New Zealand has dedicated part of its mid-band spectrum to enable the service. "

This says its only One (formerly Vodafone) customers.

edit: I notice the FAQ says something different and contradictory (which is what the parent mentioned), I wonder which is the truth?