SATs don't test potential. They, and GREs, explicitly test general baseline knowledge in a couple of subject areas. A person who grew up in poverty is still going to do poorly on a standardized test unless they have committed at least some effort to learning those things (whether through school, self-study, or a form of tutoring).
SAT’s don’t test baseline knowledge, they “require” it. That’s early high school math and English language. The SAT tests ability to perform cognitive tasks, like solving math problems and answering questions about passages you’ve read. If it were about knowledge, the questions would ask about facts.
I only know about the math subject GRE but it certainly was testing problem solving ability moreso than knowledge, many of the questions designed so that the clever can solve them quickly to save time.
