"Essentially."
It appears that your issue is with the availability of coaching to those with the drive and ambition to obtain it.
It's not about drive and ambition. It's about family money. If person A is holding down an evening job to help the family make ends meet, and person B is using that same time receiving professional one-on-one test prep, and they score anywhere nearly each other, a university would be wise to bet on person A.
I would like to know who told you that "rich families are a lot more aware of the option to get a friendly doctor to diagnose the kid with a condition that allows for an untimed test."
The rich families I know. Presumably you don't know any, or you'd be aware of this.