They look at those things for a number of reasons. Social and Economic Status, for one, which is separate from how much money one earns. The address, the level of education of both parents, the school, all tell the AO quite a bit about the advantages a given student has.
There was a “tell all” book written some years ago, “A is for Admissions” written by a former Admissions employee at Dartmouth. She addresses this issue.
Contrary to popular belief, many admissions staff members are not out looking for well to do students. Particularly at colleges like Dartmouth, where they are a dime a dozen. They are looking for students who have exceeded what is expected in their environment.
If your father is a partner at a top law firm, your mother has a PHD in education, I think you have quite the advantage over a kid with non college educated parents, working at blue collar jobs even going to the same school. That you get a plum summer internship shadowing an attorney is less than amazing in this context when you are so privileged.
Also, AOs want to know who they are dealing with as much as possible. Some apps are flagged for potential development, celebrity, relationship reasons.
Those selective colleges that are need Blind in admissions do not waste their time trying to guess whether the student has applied for financial aid or not. Admissions has enough to do in sorting out who to accept with their goal criteria.