The quote isn't about integrity. As you note, every conference has issues there. The point of the quote is that some schools , including essentially all the Big Ten (except Wisconsin), have higher standards for athlete acceptance than the NCAA minimum. At Minnesota, for example, you can meet NCAA requiremetns but still not get accepted. I can't speak to how or whether those standards get bent, although I do know that the U allows a certain percentage of it's entrants to be below it's normally very tough general admission standards, both to give kids a chance and to facilitate the admission of athletes. Of course some athletes would also meet the first (higher) academic standards, but most would not. even so, there are some who meet the NCAA rules but who still cannot meet Minnesota's second threshold.
While I can't speak to every SEC school, my understanding is that the majority simply use the NCAA minimum as their threshold for admitting athletes.
That part in bold is the problem. There should be no facillitation on the basis of athletic prowess. You can't stand above the fray, no matter if you're standards are higher than the bare minimum, because you're still manipulating entrance requirements for the sake of the success of your football and/or basketball programs.
I'm not going to even touch the issues of what happens once these borderline athletes get on campus. The Ann Arbor paper did a series on this issue last year and it illustrates what I'm talking about: You're there to play ball and to stay eligible. Academic concerns are, for the most part, secondary to that goal.
Like I said it can be noble in a way, to offer an opportunity to someone who would not have it otherwise, but we can't file it under altruism or concern for the well being of someone because of the tangled economic factors that are involved.