The only way would have been for them to do a student survey…so results are suspect. There is no way to know this information any other way.
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I know numerous people who chose another school over Harvard out of ranked preference, not financial or other reasons. They either got accepted to both Harvard and the other school and picked the other, or they got accepted to Harvard and went but said it wasn’t their first choice, which they didn’t get into. And that’s just in my single person sphere of contacts, further subset by that fact coming up in conversation.
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At our high school, in terms of elo ratings, often Harvard ranks below Princeton and Yale. You can also see where the top kids in the class apply EA to. It is often Princeton / Yale over Harvard. Or MIT / Stanford over Harvard for EA. On the margin. It also depends on the personality of the kid.
This forum emphasizes admission to highly selective, private colleges, so you get an overrepresentation of persons who are focused on admission to highly selective, private colleges. Typical non-selective public HSs often have a different atmosphere, with a greater emphasis on in-state options, particularly in state publics.
For example, at the HS I attended, the most applied to schools by far were SUNYs. The nearest community college was also quite popular. I know some outstanding students who started at both. Among Ivy+ type colleges, Cornell was by far the most popular, which related to the HS being in upstate NY. Cornell received more applications than all other Ivies combined, by a good margin. Some of the well qualified kids did apply to Harvard each year as well, but they were in the extreme minority.
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That Harvard would win the cross admit battle with Ivies and other prestigious schools isn’t surprising. It’s still the name with the most cachet among American universities - that doesn’t mean it is the “best”, but certainly if you are looking for name recognition and prestige it is at the top.
The idea proposed by the author of the article is dumb.
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Even then, they may not know because the student admitted to both may choose not to tell either one that they were admitted to the other.
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A couple random thoughts that are germane to the article and/or the resulting comments:
Regarding cost of college… A few years ago I read an article about Harvard only spending 4% of its endowment each year, not the 5% required by law. (Why they were not prosecuted or fined by the feds for this I don’t know - let’s just chalk it up to lawyers, donations and connections.) If Harvard spent just an additional 1.5% of its endowment each year the school could cover the tuition, fees, room and board for every student, undergrad and grad. My guess is that other high endowment schools - think Stanford, Yale, Penn, MIT, Northwestern, etc. - could do the same. I know some of the Ivies have become very generous with scholarship money, especially for students from underserved groups or first generation college students.
Regarding the competition to attend Ivy League schools… About 10 years ago, the WSJ ranked US universities based on interviews with corporate recruiters. Of the top 25, 15 were top public universities like UofM, UT Austin, UIUC, etc., and only one, Cornell, was an Ivy. The article recounts how some recruiters avoided Ivy League grads because of their sense of entitlement and inflated egos. Of course, the article was skewed in that what corporate recruiters sought in new hires was not representative of all potential employers. Had they surveyed blue chip consulting firms or investment banks the results likely would have been very different. The bottom line is that attending an Ivy - or any other “elite” school - does not guarantee success, and most successful people did not attend an “elite” university.
Recruiters targeting large state flagships may be working for companies that have higher volume and not-as-elite recruiting needs and wants, and may also find that competing with the management consulting companies and investment banks at elite private colleges is a waste of time (i.e. not enough yield).
Nothing guarantees success. And statistically its impossible that most successful people would have attended an elite school since those colleges represent such a tiny portion of the student population.
The more interesting question is whether attending an elite schools results in a higher probability of success. And, further, if it is true it results in better odds of post college success, can you control for causation? For example, its possible that the same traits it takes to get into schools with <5% acceptances rates (incredible talent for some, affluence and access to connections and resources for others, etc.) would have caused a higher rate of those students to succeed whether they went to elite colleges or not. Perhaps the colleges are basically getting credit for the inherently successful people (which of course then becomes self-perpetuating as successful students seek them out).
My guess is its somewhere in-between – it’s a symbiotic relationship. Elite schools attract inherently successful people (whether due to talent, money or whatever), then continue to push those people to refine whatever makes them successful and enhances it – improving their network and access to resources, etc.
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My guess is that many parents who now prefer elite schools for their children would still prefer them, even if these schools were proven not to increase their child’s probability of career success.
I have heard parents privately express the opinion that at an elite school, their child will be more likely to end up with wealthy / high status friends and romantic partners, which would be a desired outcome for these parents. Similar to Jewish parents who want their children to spend time in Jewish social environments so that they will have a higher probability of finding Jewish romantic partners. (our family is Jewish and I know other parents who are pretty up front about having this particular goal.)
Other reasons for preferring elite schools, for both parents and students, might be related to a belief that elite schools offer a college experience that is itself enjoyable or high quality in other ways, regardless of outcome (for example some of the things mentioned by @neela1 ).
Edited to add:
I guess one thing I mean to say is that I hear students talk a lot about how a school will contribute to their career futures, similar to the students in this thread. But in private, I hear parents express concerns about who will be their kids’ friends and romantic partners. Maybe this is also coded in the term “peer quality” that I sometimes hear thrown about?
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Reminds me of Susan Patton whose provacative comments got 15 minutes of fame a decade ago:
I definitely think a school’s resources can aid in a great experience. It doesn’t mean people don’t have great experiences in colleges with less resources, just that some schools have certain extra or enhanced opportunities, often helped by deep endowments. My oldest 2 both went to high ranked LACs, but one had an endowment per capital over 2x the other. The college with the bigger endowment, for example, paid students for anything that even vaguely resembled non-academic work on campus, regardless of their financial aid status. Volunteer to be crew on a school play, you got paid by the hour. Etc. The other college shut non work study students out of every campus job except dining or calling to solicit donations (i.e. the least popular jobs) and paid nothing for most activities, even when they were huge commitments (like being editor-in-chief of the weekly newspaper). Just one example of many. Our youngest got into amazing public schools, that would have nonetheless had fundamental experience trade-offs like not guaranteeing on campus housing vs an elite private school that guaranteed it all four years despite being in one of the most expensive markets in the country in a highly landlocked campus. Etc.
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Yes, I’m not saying this is necessarily a mistaken belief 
Although I had my own experences with elite schools, this was far enough in the past that I really can’t evaluate the experiences offered to undergraduates nowadays. It may be true that these schools have a quality of experience to offer that other schools can’t provide… I don’t have enough personal experience to know.
i meant academic peer quality. i did not mean some other enhanced definition of peer quality. other people may have had a different definition in mind.
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Yep, I didn’t mean to tar you with that brush! I think it’s very clear that for you personally, the phrase has an academic / intellectual meaning.
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Deleted, redundant.
Note that a “recentering” in 1995 reestablished 1,000 or so as an approximate average score in response to a significant drop in the average score across preceding decades.
and way back in teh dark ages was when a 700 really meant something. 
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But did SAT volume increase as college-going moved down the range of student academic strength? Seems that the recentering was a response to the college admission test market shifting to include more less-elite students.
The 1995 recentering concordance is included at https://files.eric.ed.gov/fulltext/ED563025.pdf so all of the parent age posters can compare their pre-1995 SAT scores with recentered ones from 1995-2016. The verbal section had a 60-80 point difference in most of the range (the old 730-800 became the new 800). The math differences were small, except in the 300s and 400s.
The concordance tables for the 2016 redesign are shown at https://satsuite.collegeboard.org/media/pdf/higher-ed-brief-sat-concordance.pdf . The differences were larger in the middle part of the range than at the ends of the range.
500+ is grade inflation. The real average boomers were 420-450.