Sorry you were picking holes in the main thread that it wasn't clear for laymans. I figured you were still on the same route here.
Technically how it does that, You've answered your own question and it was described in the early phases of this thread.
(And outlined in the document that is signed off by the privacy commissioner linked in great detail.)
Pg 55 on.
It sends notifications to all, if it finds a match, you hear about it. If it doesn't find a match. You don't. But it won't get to anyone to even be able to be sent to others, without approval/the user uploading it.
As seen here (which most people won't read, because 'govt' even if it is more than 'it just does') https://www.health.govt.nz/our-work/diseases-and-conditions/covid-19-novel-coronavirus/covid-19-resources-and-tools/nz-covid-tracer-app/privacy-and-security-nz-covid-tracer
It's also outlined in the how guide of the app itself. not that any of those people would believe it any more anyway. Once in the mindset. They're not easily swayed.
Not picking holes at all. For most of us on here we have a pretty good handle on the the way technology works. That's doesn't apply the general population. It's not just with the likes of the Covid app, a lot of "Explainers" do a very poor job of explaining to the "man in the street" how something works. The explanation is written by someone with a very good understanding of the app or device and that understanding very often isn't dumbed down to a layman's level.