I believe your last point is correct but many schools offer up academic scholarships to offset, which I’ve read here, is extremely limited at PSU.
I, and both my daughters, graduated from Penn State. My oldest granddaughter, who was 2nd in her class at a high school in New Jersey, and was very active (sports, debate, chorus, etc.), applied to Dear Old State and was offered no scholarship money as in -0-.
She was accepted at a smaller, higher rated school in Ohio and got a very generous scholarship package. She has since graduated near the top of her class, now lives in Ohio, and gives generously to her Alma Mater.