[epsilonclose]

That is certainly a real distinction, though I think your point about immigrant families not knowing "the game" is probably the better one. If parents know how the admissions game is played, then they can throw capital (fiscal and/or social) at the problem. A non-tenured biology professor is by no means wealthy, but their daughter will almost certainly have an easier time finding a lab to volunteer at in high school than the child of the owner of a successful car dealership. So wealth is an advantage conditional on knowing the rules of the game, and you've raised an important point: a lot of families don't even know the rules of the game!