You're right about what happens, of course, but vastly over simplifying.
I live in Raleigh, NC. My wife and I have two kids, one of whom will be starting kindergarten next year.
The public school we were zoned for is ~75% African American and Hispanic. I'm ok with this, I grew up in the area and went to a "majority minority" school (though there were not many Hispanics in the area back then) as well. This school also has over 50% of the students who score lowly on the English proficiency charts. 60% of the students are on free lunch. The end of grade test scores are...abysmal. When visiting the school, the teachers were just overwhelmed with having to deal with so many non-English and other remedial students.
I want my kids to be happy at school and get something positive out of it. I just could not see sending my kids to that school. This was a very hard decision, but we moved from our 150k house to a 250k house 8 miles north. The new school is still very diverse--about 35% African American and Hispanic, but has much better test scores, an actual PTA with engaged parents, etc.
It's easy to criticize those 1%%er fat cats and their slutty wives, but really, everybody wants the best for their kid. You can't blame parents for doing whatever they can--moving, paying an arm and a leg for private school, etc--to help their children out. It's really just human nature.