That is the distinction I was attempting to make. I perhaps conflated two different meanings of "assimilation." I favor the sense of living in respectful harmony with the local culture while not surrendering one's own cultural heritage. I don't favor the other meaning by which some people use "assimilation," as the immigrants conforming completely to the local culture. I thus prefer “integration” for the former and “assimilation” for the latter.
I have the same sentiments as you express in your comments about life in Mexico. I am terrible at foreign languages, but I make an effort and that is appreciated by people. The cultural dynamic of Czech and American has to be quite different than that of Mexican and American because of the vary different history or national relations. I've seen very little tension between respectful American foreigners here, though I have seen a few disrespectful American expats.