I think how one does on the SAT mainly depends on how good of a test taker someone is. I don’t think you need boarding school rigor or curriculum to do well, and I also think studying and prep can only get you so far. It probably helps those most who are nervous test takers. My kiddo at public school took the SAT and ACT after just a few sections of kahn academy self study, and having taken the psat and pre-act. She could have been one and done and has scores that are at or higher than Ivy averages but wants to take them again. Then I also know private school kids who don’t do nearly as well and have spent thousands on fancy prep classes. 
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