False dichotomy. Can't you think of any alternatives?
In Canada (not sure about other places) they often contrast the tossed salad with the melting pot. In a tossed salad, there is distinction without separation (no ghettos yet no assimilation).
Of course these are both metaphors and we can argue about reality, but surely you can at least conceptualize two distinct cultures living together without race riots. Realistically, swathes of the US are like that, regardless of the melting pot metaphor.
The dichotomy is not false, it just simply hasn't come to fruition yet. If we look to history when you have large numbers of people from different ethnic or cultural values coming together one of two things must happen. They all blend to form a new people or, in the best case, they live together with mutual tension and the occasional flare up and/or war.
It is not possible to be both one people and many. You can have a country made up of many different peoples. You cannot have a Nation made up of such.
The American model is not a loss of all distinctiveness. It is a subsuming of their past beneath their current home. They come here and become American, the shared ideal we all in theory hold. If other places can't mange that maybe that says more about them than it does about the US, no?