Kiwi here. They live in alpine regions, they have adapted to alpine life - how are they not alpine parrots? Go back far enough and you could make this argument about anything.
Domestication ≠ habitat classification.
Alpine refers to habitat. Kea live, feed, and breed in alpine environments and are behaviourally adapted to it.
By your logic, because my ancestors ~300 years ago aren’t from New Zealand, I’m not a New Zealander.