I agree, this writer seems is generalizing hostility to "ivy league" with hostility to "elites" in general.
It frustrates me that Americans still tend to view Harvard (or maybe Yale) as America's most elite university. It is an extraordinary organization, of course, but it is (strangely?) MIA in engineering and many branches of applied science. Consider the US News and World Report's list of "most elite undergraduate colleges":
Harvard
Princeton
Columbia
Stanford
University of Pennsylvania
California Institute of Technology
MIT
Dartmouth
Duke
University of Chicago
Now look at the top ten research institutions in Engineering overall..
MIT
Stanford
Berkeley
Georgia Tech
University of Illinois (Urbana)
Carnegie Mellon
CIT
University of Michigan
University of Texas (Austin)
Cornell
So there's only one ivy here, and it isn't an especially high ranking ivy in the ivy pecking order.
I don't think people resent wealth at all in America. People have huge admiration for Andy Grove, Sergey Brin, and Larry Page. They have less love for Zuckerberg, but that's because they see him as a punk kid, not because they hate his product. There's plenty of respect mixed in there too.
To me, if you want to say Americans hate people who went to elite institutions, I'd ask: which elite institutions? The elite engineering schools, or the ivy leagues? Ok, maybe some "anti-intellectuals" may brag that they didn't go to Yale (which is stupid, I'll admit). But how many brag that they didn't go to University of Michigan, Illinois, or Texas?
I think it comes down to the notion that wealthy people are wealthy because they created wealth. Once an elite is viewed as a parisitic aristocracy, the admiration drops off a cliff. As it should...
... that said, I do think it's unfair to paint the Ivy League completely with this brush. But it is telling that these venerable, elite institutions have been surpassed by such a different (and often publicly supported) group of universities.