That's simply not true. I'm not so familiar with the fauna of Hawaii, but you can consider the moa which was happily ensconced in New Zealand for about 20 million years, and extinct within 200 years of the Polynesian settlement in the late 13th century. It's pretty clear to me in a situation like that what was native and who the invaders were, and I'd be surprised if the situation in Hawaii were very different.
I suspect that the parent poster is talking about the geology of Hawaii.
New Zealand was part of Gondwanaland, and became isolated by continental drift. Anything living there when the islands became separated from the rest of the supercontinent is native.
Hawaii is a bunch of volcanoes that sprung out of the middle of the ocean. There were no land animals on the islands when they first became islands.
Now, that's a slightly topsy-turvy definition of native, which (etymologically) should mean any species that came into existence on the island.
That's simply not true. I'm not so familiar with the fauna of Hawaii, but you can consider the moa which was happily ensconced in New Zealand for about 20 million years, and extinct within 200 years of the Polynesian settlement in the late 13th century. It's pretty clear to me in a situation like that what was native and who the invaders were, and I'd be surprised if the situation in Hawaii were very different.