I think that interpretation relies on the notion of assimilation and segregation as existing dichotomously, which I'm not convinced is the case. As I said before, "integration" does not necessarily imply assimilation, but can refer to a heterogeneous society in which atomic individuals form fluid relationships through shared culture at all levels. One can be American in this context, Asian in that context, a Catholic, a Metallica fan or a Microbrew enthusiast in others. Presenting it as a choice of how many homogeneous monoliths we construct is just over-simplistic.
That's why I think America genuinely is an effective example of a multicultural society- looking at not merely the range of diversity but the depth of diversity it is capable of representing, motivated above all by the recognition of the individual as the base unit of society, shows how such a thing is possible. It's just that, as I said, the only place where this really seems to be an issue in the country are were monoculturalists (on either side!) decide to butt heads and make the whole country look bad.