Strictly speaking what you're saying is true, but it ignores other realities of the association of wealth and education outcomes which are implied when folks are talking about these subjects.

One of the best places in America to get education happens to be free: the public school system of Lexington [1]. But you'd be hard-pressed to get a house there for less than a million. Secondly, every other student in Lexington happens to have private instructors on the side. It's funny, if you randomly walk into a Starbucks in Lexington, chances are very highly you'll see an elder person with a young person training for standardized exams.

[1]: https://www.nytimes.com/interactive/2016/04/29/upshot/money-...