What they're describing is well documented, but my understanding is that the reality is a blend of what you're describing and what they're describing.

To this day there's significant social pressure to not acknowledge how much racism and racial division played a role in them growth of suburbs in the US, but ultimately it's the documented history which is revealed to those who research the topic.

In many cases individual families were not overtly racist but they were caught up in the economic effects created by racist dynamics and felt they had no choice to go along. If property prices in your neighborhood are decreasing, because neighbors are leaving, and you have the means would you not feel compelled to leave to somewhere with rising property values? Real estate firms intentionally tried to create waves of fear to get people to rush to move, selling low, and then profiting on selling to newer Black families.

It was common for suburbs to have deed restrictions limiting areas by race, and for a while federal housing guidelines would not underwrite developments that did not racially segregate.

At the same time there were massive amounts of state & federal funding pouring into suburbs and highly disruptive unpopular overhauls occurring in cities while cities were also losing tax revenue. For people with the option the future of good living seemed like it was in the suburbs independent of segregation, but part of what fueled the frenzy was the racial segregation.