Schools vary (manipulate?) their interpretations of Expected Family Contribution based on a variety of factors. The EFC at one school can vary wildly from the EFC at another school. Seems strange, but that's how it plays out. Schools with fewer resources tend to expect greater family contribution somehow ...
But here's a web app on the Princeton website that actually shows you what you would pay to send a kid to Princeton:
http://www.princeton.edu/admission/financialaid/estimator/
Here's the equivalent page for Yale:
http://www.yale.edu/sfas/finaid/calculator/index.html
I just put a scenario into each calculator for a family making a combined income of $120,000, that has some savings, and has three children. The different answers were ~$3,500 and ~$5,000 in EFC. That seems extremely reasonable to me.
Regardless, the point is that it's strange for hyper elite educations to be more affordable than state educational options, which they are. Yale, Princeton, Harvard, etc. try really hard to make it so that anyone who is accepted can afford to enroll. But getting in is both very, very difficult and (admittedly, on the part of admissions) somewhat arbitrary (out of the pool of qualified candidates, which is usually 3 times as many students as they can admit).