I want to quote these things specifically because they touch on what I said at the end of my original post, that the humanities is a qualitative field and how, in my view, this makes the notions of 'identical' and 'perfect' applications fairly arbitrary. When I say that the admissions process is political that is something else, but it plays a part in the qualitative thing--i.e. a big selling point for a good candidate is that they've learned how to think, talk, and write in the appropriate manner, the way politicians or businesspeople do. Much in the same way that we talk about presidential candidates 'being presidential', I believe one of the most important factors for admitting a graduate student is his/her demonstrated ability to play to the audience that is the academy.
Now obviously that is more likely to happen if a student attends an elite institution, because the stakes are higher and there is a great deal more investment in maintaining a certain status quo within whatever field, whether that status quo is ideological, or whatever. You asked about my MPhil; I did my master's in English at Cambridge. This is a world-renowned institution, but the Oxbridge way of doing things is something that is in my opinion highly suspect. You could see it with the strikes related to pension cuts and the scandals surrounding Priya Gopal--these incredibly prestigious institutions just know that they are so insulated from the outside world because of their name that they can get away with basically anything, and there is a lot of strategic interest on the part of faculty to engender that same understanding of cultural invincibility in students. To pick up on this in applications (i.e. in the linguistic nooks and crannies of essays, SOPs, and letters of rec) is not easy, but we are talking about highly trained people overseeing adcomms, and I'm certain they know how to spot when someone is properly conditioned. The point I'm trying to make is that I don't think this halo-effect of 'prestige' on an application is automatically endowed just by having attended a school--it must be consciously recognized and cultivated, and ultimately expressed through language and behavior. If you are not able to do that, you are less likely to make valuable contributions to an elite institution's record. I agree completely with your remark about 'hard work pays off' being basically bogus, but only because hard work is circumscribed by the privilege that precedes it; if you possess that privilege, or you've figured out a way to imitate it holistically, then your hard work becomes effective.
Look at what's happening with the Harvard lawsuits for example. The results from the court proceedings show that Harvard's admissions overseers literally think Asian people are 'too boring' to contribute to 'campus culture'. But how does one adjust their personality for a university, and how does this eventually play into this idea of a perfect application beyond what has been deemed necessary, those things that make two applications appear 'identical'? My evidence is indeed anecdotal, but when I was hanging around English phds at Berkeley (where I did my undergrad) their manners and topics of research were unmistakably influenced by some external force, some larger corporate-like culture. They saw what Harvard sees in these 'boring' applicants: they don't know how to play ball.
(As for my acceptances, I'm not an English PhD applicant. I'm an interloper from Communication, where in my experience safety schools are more commonly acknowledged.)