I was just wondering what they would think.
They look at candidates in the context of their schools. A top student at a top private may be more of a known quantity (i.e., no doubt they are well prepared and can handle the work) but a student who has thrived at a so-so public may be able to make a better case for making the most of opportunities and applying himself when it may not be the norm. Neither is preferable.
This is one of the reasons AOS cover a region - so they understand the context.
Each high school sends a school profile along with the transcript so the applicant can be reviewed in the proper context.
It’s not that simple but each applicant is viewed as an individual first, his own application. Then there can be some context consideration. Eg, it’s good to have certain experiences. But some top preps are known for facilitating these, actually connecting their students to opportunities. And not all kids at top preps are necessarily either top academic quality or go-getters. They get steered toward the right colleges for them.
The biggest advantage of private schools is that often their college counselors have developed relationships with the admissions officers and can better advocate for their students.