Kind of missing the point of what it means to "get it under control"
You will have spread no matter what you do. The question is how much.
If prevalence of the virus is high, then the risk of spread is higher. At a high level of prevalence any systematically repeating and mixing groupings of people (such as school) is pretty much guaranteed to lead to an outbreak, which will stop or at least seriously disrupt and hinder that system (not to mention the sick and dead people from the outbreak).
At a low level or prevalence outbreaks will still occur, but only here and there. Some schools will have outbreaks and have to stop, but most will be able to keep going.
Widely available tests with fast turnaround is also part of this because it allows outbreaks to be detected earlier, when they are much smaller, which limits the disruption each outbreak causes (not to mention the deaths and sickness).
The point of all this is to have most of our normal activities and economy until a safe and effective vaccine is widely available.
Did they confirm this? I could also see issues with someone asymptomatic who was quarantined, but was at the 99th percentile for incubation period. With an R0 near 1, with enough people, you could miss the virus for even a few months.
It's really hard to contain, and NZ will likely be dealing with case like this on and off until there's a vaccine.
Read about 'flattening the curve'.
(All from a US perspective)
There's been a crazy notion floating around from the start on this, that we can either keep our normal activities/economy (jobs, businesses, schools, etc) or deal with the pandemic.
However, you can't have anything normal unless the pandemic is under control. Because until it is, so many kinds of normal activities will be hit by an outbreak, and then your normal activity will fall apart and stop.
I think we could have had school this fall. But it would have meant much more serious efforts months ago, building up our fast testing capabilities, a commitment to ongoing mask, social distancing, and other mechanisms to control the spread (mandates, really).