20,000 yes. 30,000… probably not. Where are you getting your source for "probably more like 30,000 years?
Easter Island wasn’t settled from New Zealand, though, but from closer islands. And nowadays, it looks like it was settled only in the last millennium, so wouldn’t be the source for South American prehistoric settlers. While there are some signs of pre-Columbian contact between South America and Polynesia (Sweet potatoes, for instance), Polynesia itself wasn’t settled early enough to be contributive to the prehistoric South American population.
I see nothing too wild about the idea that the same root population that founded the Taiwanese aborigines also contributed to the first pulses of human settlement through Beringia.
