I think therein lies the disparity I see a lot in talking about "diversity" between some Europeans and some Americans: here, we generally view diversity as a plurality of races, whereas it seems (to me) in Europe it is seen as a plurality of ethnic groups.
[EDIT: What deserves a down-vote here? Does racism not differ from ethno-centrism? Can we not have a reasonable discussion on the point of the person I am responding to? He points out that welfare has nothing do with racism in Switzerland, because they're so well integrated with other races, yet does not provide any evidence to that point. My statement was clear, not argumentative, and as far as I can tell completely non-combative. If you disagree with my statements, then please tell me why, so we can have a discussion.]
In fact, for major parts of Europe it was never true in the first place, the continent has seen centuries of migration of various ethnic groups and cultures before many of today's nation states were even formed.
Pointing to European countries "homogeneity" is just a cheap and borderline racist (they're all white people right, so how can they be ethnically and culturally different?) excuse used by Americans that don't want to examine their own motives.
To have a migration background does not necessarily to have a different ethnicity.
Also, in Switzerland's case, it would be worth mentioning that the (cultural but also the ethnic) diversity was always a little higher than a lot of other European places and somehow they learned to handle it pretty well.
Interestingly enough, this is not true for Switzerland. In some cantons, up to 60 percent of the inhabitants have a migration background. (i.e. they or their parents were born abroad) [1]
[1] http://en.wikipedia.org/wiki/Immigration_to_Switzerland#Popu...