Aren't a lot of people allowed to recover and isolate at home? I recall the cases in Wellington were. Maybe it is something to do with other cases in the home, where if there are a lot of people living in a household, it is more than likely others will be infected too, or they could be infected if the person remains in the house. If people knew more details and there was more transparency about what happens if someone tests positive, there maybe a lot less anxiety about it.
The process is completely transparent. It requires a 5 second google search to learn about it.