Manhattan households are 76% car free
Brooklyn households are 56% car free
And these are reasonably prosperous people, by national standards
http://blog.tstc.org/2017/04/21/car-free-new-york-city/
But there's also no question that
poorer households tend to be more car-free.
Even so, for the rich household, having 1 car, good for a getaway to the Hamptons or the Catskills can still mean that one household member gets "the car" and another has to make the trip by train. This is still a powerful contrast to the rest of the USA where we're converging on 1 adult == 1 car.
The Manhattan rich dudes I know have 1 car kept in the city, 1 car kept at the country/beach/mountain house, and "the family" takes the city car, full of kids and stuff, out to "the house" when the kids are not in school, while "the dad" who lives in "the apartment" joins by train (or plane) later (and "the dad" only drives a car when not in the city, and not to-from the city).
So I'd say that even the "1-car" (or only-1-car-in-the-City) households can still be considered "affluent adults without a car" at least some of the time.