They are not key determinants. There are places in america you will see kids outside doing things. New urbanist developments, core of college towns, neighborhoods in big cities, ... And this is because stuff worth doing for kids is safely accessible without car there.
The big intellectual tragedy of the 2nd half of the 20th century is that we have become blind to the fact that much of our behavior, aspirations, dispositions are technologically determined, and not the other way around.