I can really see both sides of this. I understand why they are picky about where they place animals, because they have seen the dog be returned and/or mistreated. On the other hand, it makes some of us very shy of going to a shelter or rescue. We adopted our dog from a pound, and about 6 years ago, I went with a roommate to adopt her dog from a pound.
When my roommate and I were looking, we went to several shelters. Most were very hesitant to adopt to us, or wanted our parents permission (dare I mention we were 24 and 27, and living away from home for 6 to 8 years!). We finally ended up at the local animal control office and found the best dog ever! And the guy who ran the place was so happy we wanted to take on of his dogs. It was so different than the other 3 shelters we went to.
What I took from this expierence is that if you want a dog with few questions asked, go to a kill shelter. And sure enough, when DH and I were looking, we ended up at a local animal control. We found Zoe and fell in love. She was $65 including vetting, first shots, and $30 off the spay. No vet checks, no asking us about our house (other than rent/own). The local no-kill shelter we tried first wanted vet references, home visits, etc. We had just lost a cat (through no fault of us), had no fence, and let our cats out. We weren't formally denied, but the look in their eyes said we weren't getting a dog. And heaven forbid you are ever turned down, every other rescue application asks if you have been turned down before.
So we now have Zoe. We have had her for about 2 months now. She is spayed, healthy, and a great dog (except its rained for 3 days straight and she is going stir crazy!). We have our fence half built (see bit about rain). Our remaining cat still goes out some, but is getting along as well as can be expected in the house. Plus, I know that we saved a life in the process
I still tear up thinking that if we hadn't come along, she might not be walking the earth anymore.