I don’t think that’s true. Lets say you go to to one of the public schools that’s middle of the pack. I think the rankings were 1 to 97, so you’re at the #48ish school. Your parent’s, and your parent’s parents don’t have to be rich for you to get a good education there. If your parents raise you to know that you need a good education to go anywhere in life, you’ll get a good education. You’ll go on to college and do well there as well, even if you have to work part time and take student loans to do it.
I still think the fact that rich parents kids do so much better is the fact that most rich parents got that way BECAUSE of their education, so they raise their kids to strive for a better education as well. Sure, there are advantages when mommy and daddy can hire an expensive tutor if their kid is having trouble, but that isn’t absolutely needed. That vast majority of the kids that are doing poorly in public schools could be doing fine if their parents just took the time to be involved. Punish little Billy when he fails his math test. Make sure little Billy is doing his homework, find out when his tests are, and make sure he’s studying for them. Parents who know the value of an education do these things, and their kids do well regardless of income.