Oldchild,
I have lived and worked in the education industries in both Taiwan and mainland China, and I can say that you have hit the nail on the head here. Wealthy Chinese pay tons of money to get their kids the sort of tutoring you describe.
Also, many of the poorest people in China, the migrant workers, have not even been eligible for public schooling, since they are not legal residents of the area. Their kids must attend migrant schools, often substandard, which are very expensive for the families. Even children who are eligible for public schools sometimes cannot attend for financial reasons.
It's disingenuous to claim that Chinese kids have equal opportunity because they take the same test when they've had unequal opportunities to prepare for that test.