DoC's advice and communications with the Minister on Wicked Campers are here. The short version: the Minister of Conservation asked them if they could ban Wicked from their campgrounds, and they said "no". Instead, they suggested that local bylaws could be used where applicable, but pointed out that this wouldn't work either, and would likely lead to a rise in freedom camping. Their conclusion was that DoC was not the appropriate agency to deal with this issue. But while they addressed freedom of expression issues in the context of bylaws, there's no specific acknowledgement in the written advice of DoC's core obligation to act in a manner consistent with the BORA.
But there's also a smoking gun:
(And from that earlier news report, the internet team complied)
Just to make this clear: the Minister (through her office) directly called a tier-3 manager and asked them to fuck over a business (AKA interference in an operational matter). And they complied. From the context, this act was specifically performed as a punishment for speech the Minister did not like, and to the extent that DoC's website is effective in informing tourists (something I'm sure they'd want to claim) intended to and effective in inflicting commercial harm. Which is at least two lawsuits waiting to happen. And if Wicked sues and wins, the blame for that will rest firmly on this interfering Minister.
But this isn't just about Wicked. Because what Ministers can do to an unpopular foreign camper-van firm, they can do to anyone. Such as companies which criticise government policy, or companies which donate to rival political parties. You might want to think about that before mindlessly supporting Ministers using the machinery of government as a weapon against their political enemies.