That may be true to a point, but the issue is not mere statistical diversity i.e. the probability that two randomly selected individuals belong to two different ethnic groups (aka the heterogeneity coefficient). Far more important is what for the lack of a better term I call "cognitive diversity" or tolerance of and interest in groups different than one's own. Unlike the statistical diversity, which is simply a probability function and thus continuous, the cognitive diversity is context dependent, discrete, and selective - one may be open for diversity of one kind but not for another, or openness for diversity may be correlated with other forms of social diversification, such as socio-economic class, collective mythologies pertaining to different social groups, past experiences, etc.
What you are referring to is a specific type of cognitive diversity maintained by the officialdom (i.e. official recognition of various ethnic groups) , which is relatively absent in the modern US comparing to, say, Japan or Europe. But unlike statistical diversity, cognitive diversities cannot be compared because they are qualitatively different - since they are grounded in perceptions as much as in reality. What is more or less diverse a mild intolerance of most other groups (which on average characterizes the US) or tolerance of some but intense intolerance of others (which characterizes Russia?
Wojtek