The "deal" they refer to is that agreed between Key and his then counterpart Julia Gillard in 2013, providing Australia with the option of placing up to 150 refugees for resettlement in New Zealand a year. The arrangement echoed an earlier deal which saw New Zealand take in 401 people from Australian offshore detention centres between 2001 and 2007, with more than half of them having been earlier rescued from the Norwegian tanker Tampa.
When Tony Abbott became Australian PM he doused the deal, citing the risk of incentivising so-called "boat people" by creating a "consolation prize" across the Tasman. As Woodhouse confirmed last week, however, it remains formally in place, though any arrivals would have to come out of the annual quota of 750, currently accounted for by Syrian refugees.
Late in 2015, Key confirmed that while "Australia hasn't exercised their right there ... that's always an option that's available".
In a follow-up letter to Malcolm Turnbull published this week, the same group of refugees explicitly reject the suggestion they might use New Zealand as a back door to entering Australia. "Many of us do not believe that Australia respects human rights any more," they write. "Australia does not even respect the rights of your own Aboriginal people."
With asylum policy a populist powder keg in Australia, both main parties are dead against providing refugees arriving in boats with a chance to resettle in their country. Instead, under hardline immigration minister Peter Dutton, they are set upon dispatching the asylum seekers to developing countries, such as Cambodia. So far, that has proved a pricey exercise, with five refugees deposited in Cambodia at the mind-boggling cost of $55 million. Cambodia, write the Nauru refugees, "does not offer us security or a safe future, either. Cambodia only accepted the deal for the money".
Nor is there either security or safety in Nauru. The entire Australian offshore detention experiment, encompassing Nauru, Manus Island and Christmas Island, has been plagued by controversy since it was established post-Tampa in 2001.
Life for refugees released into the Nauru community has by most accounts been little better.
Once given the inadvertently sinister name "Pleasant Island", distant and isolated Nauru, less than a quarter of the size of Waiheke, is the world's third smallest sovereign state, behind only pretend-states Vatican City and Monaco. Nauru is arguably little more than a pretend-state, so dependent has it become on aid from Australia since income from phosphate mining dried up.
In 2012, shortly after Australia reopened the Nauru camps following a five-year mothballing, Amnesty International inspected the facilities, finding "a toxic mix of uncertainty, unlawful detention and inhumane conditions ... a human rights catastrophe with no end in sight".
Horrifying reports of institutionalised violence and intimidation, sexual abuse and even rape have become routine.
Numerous reports have pointed to the devastating long-term impact on refugee children's mental health.
In October last year, leading Australian health agencies condemned the absence of monitoring of health in offshore detention centres, which had "contributed to ongoing incidents of mistreatment and human rights abuses". They noted that the Australian Government failed to act on monitoring despite the concerns being highlighted by "a succession of parliamentary inquiries, royal commissions, coronial inquests, and reviews from international bodies".
Boat numbers - as scrawled beneath signatures in the letter to New Zealand - are widely used instead of names by guards.
According to submissions by former workers to a Senate Inquiry, many children have begun to identify more by their numbers than their names, signing school projects with the six-digit codes.
Australian politicians have at least been efficient in dealing with the perils of whistleblowing. As part of the Border Force Act of 2015, workers who disclose any "protected information" risk up to two years' imprisonment. In September 2015, the UN special rapporteur on the human rights of migrants cancelled a planned trip to Australia, saying the legislation made any credible investigation impossible.
There is little cause for faith in the Nauru regime itself: following repeated criticisms of the island state's justice system, New Zealand Foreign Minister Murray McCully last year suspended aid, citing issues around the rule of law and the treatment of opposition MPs. McCully also expressed concern about access to justice for asylum seekers.
When Australia's record was reviewed at the UN Human Rights Council in Geneva in November, the country was roundly criticised for its detention policy (including, it's fair to say, by countries with considerably more shameful human rights records). New Zealand's submission was meek, making no direct mention of detention policy, nor the New Zealand citizens on Christmas Island.
Asked about New Zealand's failure to speak up, John Key said: "We do not need to go to Geneva to do that; we do it in person with the Prime Minister of Australia."
Perhaps he is regularly berating the latest Australian PM over these deplorable Pacific Alcatrazes in private. But maybe - if for no other reason than because it is the right and moral and decent thing to do - he should more publicly condemn what the Melbourne Age this week described as an "ignoble, demeaning and eternally shameful policy".
Naively or not, I like to think generosity of spirit in the face of xenophobia and intolerance holds stronger in New Zealand than it does over the Tasman. The Nauru letter writers seem to think so. This is their request: "Will you honour the deal with Australia and issue us with visas for New Zealand to travel and allow us to permanently settle in your country which can offer us genuine safety and protection? We only want to build a future for ourselves and our families in a just and safe society and a country that upholds human rights."
