When is an organisation subject to the Official Information Act not subject to the Official Information Act? When it has a secrecy clause. When John Key said publicly that he had written to the Remuneration Authority "expressing my view that there should be no increase" in MPs' pay, people were naturally curious as to exactly what he'd said. So they used FYI, the public OIA request system to ask. The Authority is listed in Schedule 1 of the OIA, so you'd expect a response. But according to the Authority, s9(1) of their Act forbids them from giving one. So, the Remuneration Authority is explicitly subject to the Act, while not being subject to it. Its absolutely bizarre.
As for how we ended up with this situation, this is a legacy clause, dating from an era when we still had an Official Secrets Act. And as it deals with sensitive issues of how much people are paid, in that era such a clause probably seemed like an appropriate way of dealing with the privacy issues. But the Remuneration Authority is not the IRD and it is not WINZ (both of which have similar clauses, because they deal with heaps of deeply private information); it handles abstract questions of how much classes of people should be paid, not deeply personal questions of individuals' personal circumstances. To the modern eye, the secrecy clause is outdated. To the extent that there are legitimate questions of privacy and the need to receive submissions in confidence, these can be protected under existing OIA withholding grounds. While it won't help this request, the Remuneration Authority's secrecy clause is outdated and should be repealed.
(As for how to solve this specific problem, there's two ends to every conversation, and where one is legally secret, you can always ask the other).