The thing is that it may or may not be something “random” that tips the decision one way or another for an applicant. I think it is at least as accurate to say that admission can turn on very, very small things. A phrase in an essay or an LOR, for example – and what is NOT said (or is between the lines interpreted or implied) can carry a lot of weight. I think a lot of applicants are never aware of what that small thing is that is causing an issue at top schools, even if they have very good stats. I especially find that teenagers are (honestly) awful judges of what is a good essay, and how it comes across to an adult reading it. Depending on who they pick to review their essay (if they have anyone look), that person might not be a good judge, either.
And then there are things out of the applicant’s control (gender, for example, or how many hooked applicants have already taken slots). They aren’t RANDOM – but they are not in the applicant’s control, either.
All of this is why it is important to have matches and true safeties that the applicant wants to intend. Unintended errors in the application and/or forces outside the applicant’s control conspire against their odds of getting accepted to reach schools.