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This has been discussed many times and I can speak from insider knowledge that applicants get reviewed by someone familiar with the part of the world they are from. That is, we have two professors who review Asian applicants. Another who examines European, another for South American and then regular adcom members examine the North American applicants.
There are a hugely disproportionate number of applications from International students, however most of them are "bogus", as in they have some aspect of them that indicates they are not at all suited to grad school in the US, and that perhaps they are just seeking a US visa. (I have been told this directly from a past DGS at Pitt). Once these are removed, there are more realistic domestic applicants than internationals.
The cream of the crop from each international region gets forwarded to the main adcom with an explanation of how such a student compares to a US student. While internationals may have more credentials, American students tend to catch up quickly and often surpass the internationals - on the job market specifically. So credential differences matter less than you think. Adcoms want to admit students who will proceed through the program at the correct pace, and then land a good academic job. American students will often start slower but are better at writing papers and presenting their work, are more popular as RAs (from my experience) and do better on the all-important US job market.
Saying that there is some quota of positions is not really accurate, it's just in any group of 500 applicants, the shakedown will look similar as the applicant pool is on average very similar each year.
* Note, I am not American.