Elite private schools can offer good financial aid, but it’s far from guaranteed. Even the net price calculator is only a rough estimate and is far from a guaranteed amount. You can’t depend on a private schools financial aid generosity.
If you’re low income, I would highly recommend a scholarship. That’s financial aid you can count on. Check out University of Alabama, Auburn, Ole Miss, and Miss State. They offer the most generous out of state scholarships as far as I know. With a 4.0 and an ACT score of 34, TCU offers a university guaranteed full tuition scholarship.