In all disputes such as the one currently raging in the Letters column on Pre-Maori settlements and the like, it pays to define one's terms before one winds up talking nonsense.
The Moriori are the indigenous Polynesians of the Chatham Islands. Their language is as closely related to New Zealand Maori as is Cook Island Maori.
They never at any time settled on the New Zealand mainland.
The Polynesians are the original explorers and inhabitants of the Pacific Islands, including New Zealand. I've read Maori stories about canoes making landfall and discovering that the people who preceded them were starving, living on fern-root - but since the two could talk, and the newcomers also shared their kumara, thus enabling the earlier arrivals to live long enough to be integrated into the newcomer's tribe, the first arrivals were Maori as well.
The Chinese explored the Pacific, but they were more interested in the Indian Ocean - more trade, more money. And then the Spanish and the Portuguese, then the Dutch and the British turned up. Until the Melanesians developed the outrigger canoe about 3000-3200 years ago, nobody in South-East Asia could even dream of crossing the Pacific Ocean. And nobody anywhere else on the planet was even close to having such a set of skills until the last few hundred years. The Mediterraneans were strictly coast-huggers.
And don't get me started on the idea that the patupaiarehe preceded the Maori - patupaiarehe means forest spirit, fairy, and the like, in Maori culture. Anyone who holds that particular view is, umm, 'off with the fairies” ...

Wesley Parish, Otumoetai.