As an aside, those you refer to as "indigenous Polynesian people" are actually a later wave of Tahitian colonists who conquered and oppressed the previous settlers from the Marquesas Islands.
While again being technically true, I would love to see any white or asian immigrants noting the ethnography of the original Hawaiian people in the time where they first made contact with and lived among the Hawaiian people.
By the time of Kamehameha, I was taught there was a unified monolithic Hawaiian culture.
Does it actually matter whose ancestors colonized first? What's the difference between Hawaii's colonization by ethnic Tahitians and North America's colonization by ethnic English?
http://www.waimea.com/people.html
So it's not automatic that this particular wave of settlers uniquely deserves to be called "Hawaiian".