Wow. I adopted Kiwi from a shelter when I was 20 years old, living alone in an apartment (had just moved in) and had two other pets already. They didn't ask for a vet reference, although I would have given it to them.
Maybe it was just because she had been there so long and was listed as a "special needs" cat, but during the interview where they supposed to be making sure you would be a good home for the cat, the time was basically spent making sure I understood her condition and then making sure I still wanted her after it was clear I understood. Maybe it was a regional thing.
I waited for a long time for the interview, and heard tons of different interviews as I hung around waiting, the only ones that were rejected were the really crazy folks, that said the dog/cat would live outside, they already had a dozen other pets, they tried to haggle about the price, etc. (Cats were $25, dogs were $50. At that shelter, they still are.)
There are so many alternatives to buying from a pet store, to be honest with you, I don't see a good reason for it. If the shelter is wary about adopting a cat to you, ask if you can volunteer there, show them that you're that
interested. Provide character references. Or, go to a kill shelter, they're usually a lot more lenient on their adoption standards, because the cats are slated for death anyways.
Keep in mind, the shelter isn't trying to be mean to you, they're trying to ensure that the cat go to the best home possible, they just have the cats best interests at heart, that's it that's all. Prove to them that you would be a good home, don't be insulted.
Ultimately, there are far too many cats being killed everyday as a result of irresponsible breeding, and pet stores support irresponsible breeding because it makes them money. Stop irresponsible breeding = stop the needless killing of so many unwanted cats. It really is that simple.
I would jump through whatever hoops I had to in order to avoid supporting that industry.