Maybe my perspective is a bit unique on this, but there are two major points I feel are missing in this article.
1) These closed searches are confidential by necessity, and the people on the committee have to sign NDAs. This is not new. The students get representation on these search committees through their elected ASUM reps. When I was in college I was on three of them at a different school in Montana. One for an AD, or to run the tutoring program, and one other that I am blanking on the position. I believe it was for the football coach. I wasn't allowed to talk about it.
Going beyond that representation is not possible when searches like this are, by necessity, closed and confidential.
2) While I understand informing students is important, I would contend that the average student has very little understanding of what would make a strong University President. For those that feel they do, their input after meeting the candidates will absolutely be considered. But there was no role for the student body as a whole to play until candidates come to campus. I'm sorry, but there just isn't. The amount of students who could give informed opinion on a search for a University President is very small, and those students are probably already just as connected to what is going on as anyone else outside the search committee.