Especially since many Westerners have similar family histories, if you count the previous generation. My Greek grandfather survived a bout of ethnic cleansing [1], a civil war in the first country he fled to [2], a Nazi occupation in the 2nd place he fled [3], and a civil war between the leftist anti-Nazi partisans and the Western-backed government in exile [4]. So he had sort of an, "eh, I've seen worse" attitude.
Lots of American Jews, Armenians, Lebanese, etc. are not in the U.S. purely for reasons of voluntary relocation, either.
[1] http://en.wikipedia.org/wiki/Greek_genocide
[3] http://en.wikipedia.org/wiki/Russian_Civil_War