I wouldn’t read too much into the boarding school T20 placement as evidence schools are need aware.
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they still are extremely selective. Their T20 candidate pool per student will dwarf an above average public.
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kids have a ton of admissions support to polish holistic apps.
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the course offerings and academic support are top notch
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families have money to even consider expensive private tuition. There are a lot of extremely well qualified students at middle/upper middle class public’s whose families fall in the wealth “donut hole”. Too wealthy for aid 150k+ but not so wealthy that 75k/year isn’t a huge burden. Those kids don’t even apply.
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legacy status. Boarding school student bodies are disproportionately legacy at extremely selective schools. That can double an applicant’s admission chances at those schools.
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ease of comparison. Colleges see a lot of apps from classroom peers over years at these schools. There’s a lot of basis for comparison. AOs know what kind of student is likely to go on to do what level of work/university contribution because there’s a rich data set there. I think this helps in borderline cases where boarding school advisory office reaches out to the AOs.
An otherwise unhooked high stats, at least decent EC kid might have a 10%-25% shot at a T20 type school, depending upon the school. With legacy, that could jump to 20-50%. Add some boarding school admissions counseling gloss and that could be 35-75%.
I think what you’re correctly perceiving is the inequity in education generally, legacy preference and some of the limitations of holistic admission rather than AOs inferring ability to pay.