You are exactly right. What being wealthy buys you is a support system of assistants and access.

The school "Admissions Coach" had personal relationships with Admissions Directors at dozens of Universities and Colleges. He could make sure that applications from "his kids" got looked at and vetted by a real human being. Instead of being thrown in the slush pile.

Getting in on your own. Much, much harder. Kudos to your son for managing it, and to you for being such a great mom.