Hi @stevensPR I’m sorry i’m not familiar with your posts about cross-admit data. I would be very interested in seeing it. If you wouldn’t mind pm-ing it to me, I’d love to take a look. I always like learning more about college admissions! That being said, I don’t disagree with the fact that parchment is imperfect, as acknowledged in my post. But for two schools like JHU and Penn, the data can be quite revealing. Comparing schools like UC Riverside and Stanford can be a little trickier, however, due to issues of sample size of cross admit data and other complicating factors that are likely more reflective of the applicant pools than the schools themselves. But again, Parchment isn’t perfect- but it is a lot of fun 
Furthermore, I’m not saying that JHU is breaking the bank, and you’re correct that JHU has far fewer resources than many of the Ivies. However, I’m saying that, like most other schools outside of the Ivy League, it uses money to lure top students away from the Ivies, of which Penn, Columbia and Brown are three. There’s no shame in that; it’s just a fact of the game. Good schools need to use what they’ve got in a highly competitive market for the best high school students.
Finally, I think Penn’s reputation really speaks for itself. And at least in Penn’s viewbook available online (http://www.admissions.upenn.edu/images/uploads/docs/U37153_15_Viewbook.pdf) I only see the term “ivy league” mentioned in the page on athletics. But either way, you’ll have to forgive Penn for situating itself among its peers in its promotional materials if you’ve seen Penn publications I haven’t in which they talk about being an Ivy. It’s not like other schools aren’t proud of their affiliation (It is indeed an Ivy and it’s particularly proud of the history and tradition associated with its inclusion in the most elite brand in higher education). And Penn is not alone - the rest of the world just tends to lump the ivies and elites together as a group.
For example, the NY times did a piece on economic diversity at US colleges and grouped the 8 Ivies and “selected elite” schools (MIT, Stanford, Duke and Chicago) together. (https://www.nytimes.com/interactive/projects/college-mobility/brown-university).
And when Slate wanted to report on how students from elite colleges were not applying to law schools in the same numbers, they chose to focus on those same universities as a group.(http://www.slate.com/blogs/moneybox/2016/03/14/fewer_elite_college_students_are_applying_to_law_school.html)
And when the colleges were asked to report on who their peers were, schools like Yale chose the 8 ivies,
MIT and Chicago (http://www.chronicle.com/interactives/peers-network).
And when a student gets into a handful of ivies, local newspapers tend to write stories about them because these schools have such powerful reputations.
I don’t think I could really elevate Penn’s reputation if I wanted to since you can’t go any higher than the top