while technically correct, it disregards a simple but important fact: cultural compatibility.
why the one time it didn't work... it didn't work? because you had a local population that was living a completely different life with a completely different set of rules and values and a complete lack of the concept of land ownership, borders and war compared to those who came. and those who came brought along a culture that could not coexist with the local culture so one of them eventually had to go... and as is the human way of making the choice, one of them was wiped out violently for the other to become dominant (and having an expansonistic policy about that culture and religion was also a major motive).
many of the so called refugees of the past were people of european descent so they had much in common with the locals of USA who are also mainly of european descent so there were few excuses for clashes. east asians on the other hand, while proud of their culture, were secretive with it and tried to keep it out of sight of gwailos. that secrecy was also the reason for them not having expansionistic tendencies that would cause a clash.
and coming to today, we have a large mass of people who follow an incompatible and highly expansionistic culture coming to the west. i wonder what part of history this makes people remember.