It's only the first generation of immigrants that aren't "native". After that generation, there is no difference in immigration status.
Thus, Nissei Japanese in California are just as "native" as third and fourth generation WASP's.
Likewise, a "white" Zimbabwean born to a familiy of 5th generation Zimbabweans is just as "native" as a "black" Zimbabwean born to 12th generation immigrants from Zambia/Mozambique.