I have heard from a few people lately that Twillo texts are getting "lost". I don't believe they have any legit links to the NZ telcos.
If you need reliable delivery, go with a NZ based provider. Not only should you get reliable, hassle free delivery, but they should be able to respond to any problems quickly and by phone if required....
Yes having local providers would be more reliable, it is just alot more work when the SMS messages are sent world wide. Twilio handle this for us, unfortunately they do not currently have New Zealand numbers.
We have had complaints from South Africa and the USA, but we get the majority from one ISP in New Zealand, interestingly usually ported numbers.
Twilio Verify would be worth looking into, if the SMS fails the user can opt for a phone call.
This video helped me understand how hard SMS delivery actually is.