I have to admit, I've not had a problem with a shelter or a rescue since my Mom and I were turned down for a kitten because we lived in the wrong county some twenty-something years ago. All of my adoptions of pets (5 of them) have gone pretty smoothly.
I think that article does hit a very important point, though I wish it would highlight it more. That point is that this question should be asked: "Is there some way we can make this work?"
Because I think what really sends people off the deep end and leads to real feelings of injustice is when there is some absolute, arbitrary rule, such as "no fenced yard, no dog" or "any intact animals, no cat." The prospective owner points out that they run marathons and excercise for 3 hours every day, and they are still told no dog (or they want to adopt an elderly basset, or . . .). The prospective owner has a SAR dog, or an animal with an anesthesia allergery, or (god forbid!) is a breeder, and they can't have an animal . .. even of another species. Or you have kids, therefore you can't have a large dog. At all. Ever.
Its one thing to flag such things as issues that need to be discussed in an interview. Its another to make them absolute bars.
For example, there was an uncomfortable moment when we were adopting Shadow, the younger of our cats. Just that morning we had had put down Bago, another cat, at the age of 11 due to kidney failure. We listed on our application for Shadow that we had lost a cat at 11. The adoption counselor looked at that and said . . ."Eleven? That's younger than we would prefer . . ." Mike responded "He died of chronic renal failure. This morning." "Oh! I'm terribly sorry. That's different." End of discussion, and we walked out with Shadow. She had a right to ask (it was young) . . . but she needed to ask, not make assumptions, which she did, and found out that there was little or nothing we could have done for Bago. That's how these things should go.