> Now, an AAMC-accredited education, on the other hand, provides a lot more parity out of the gate when it comes to opportunity.

The medical guild used The Flexner Report (1910) [1] to eliminate opportunities for people to train as doctors:

  The Report (also called Carnegie Foundation 
  Bulletin Number Four) called on American medical 
  schools to enact higher admission and graduation 
  standards, and to adhere strictly to the 
  protocols of mainstream science in their teaching 
  and research. Many American medical schools fell 
  short of the standard advocated in the Flexner 
  Report and, subsequent to its publication, nearly 
  half of such schools merged or were closed 
  outright. Colleges in electrotherapy were closed. 

  The Report also concluded that there were too 
  many medical schools in the USA, and that too 
  many doctors were being trained. A repercussion 
  of the Flexner Report, resulting from the closure 
  or consolidation of university training, was 
  reversion of American universities to male-only 
  admittance programs to accommodate a smaller 
  admission pool. 

[1] https://en.wikipedia.org/wiki/Flexner_Report

The Guild has been fairly successful at keeping the number of doctors educated just below the number of needed. Foreign-educated doctors are imported to fill the gap.