Very true - but I don't think invasion is the same as peaceful immigration.
Colonizers destroyed the way of life of those who lived through a deliberate program of "civilization" (reeducation) which included sending native children to boarding schools to be raised in American culture and "rescued" from their own.
Indian removal [0] is a decent place to start reading.
This was not cultural change via the melting pot, this was genocide and reeducation as state policy, with a generous helping of biological warfare.