@calmom It should be noted the Columbia and Barnard participate in HEOP. They admit significant numbers of low income students with lower SAT scores. Indeed, you cannot get a HEOP award if your SAT/ACT is above a certain threshold. I’d also argue that having over 50% of students on financial aid represents a significant financial commitment on the part of these universities.
Having worked in admissions, I’d also argue that students with significant financial need and with less-than-stellar academic records have a better chance at these highly selective universities because they will take the time to evaluate individual circumstances.