But that plays into the flaws in the reasoning illustrated in the (insightful) observations about Caltech versus Harvard in terms of applicant pools not being identical. I'm not sure that there is a good way to compare one elite institution to another in the first place for the simple reason that each "brand" draws a specific potential applicant pool.
There are two questions in your post.
First question is do the Ivies discriminate? The answer is yes. The numbers of non-Jewish whites and Asians admitted over time has dropped in favor of Jews and others in either absolute and relative terms. This is supported by both general population and NMSF comparisons. The only flaw I can see in the reasoning is if the number of apps correspondingly dropped for the "discriminated" populations and I would find that unlikely given how they were accepted before, all things being equal.
The second question is one of branding. I agree that Caltech and the Ivies are somewhat "local" schools. The author addresses this obvious issue by looking at both national and state populations and then playing admissions off both national and state NMSF numbers. In this case, its hard to see a flaw in this line of reasoning.
The one thing the author does miss, and it does play into school selection, is that a lot of public schools and tier 2 privates actively court NMSF students with full rides and good programs. The Ivies now have some solid competition. A number of my coworkers and friends with stellar kids chose to go this route and never applied at all to an Ivy.
On the other hand, I know from some kids here in Dallas that a lot of kids do apply to Ivies and do not get accepted despite NMSF, straight A's and and AMC Honor Roll.
And the article points out that the Ivies accept around 25% of the kids with perfect SATS. So that would tend to imply that the applications from top kids are in abundance still.
So it seems to me that the preponderance of evidence is in the Author's favor.
