Hey there, fellow BYCers!  So sorry for the long post...
I'd like to offer my perspective, with the goal of adding a different point of view, and at the same time respecting the value of differing opinions. 
On experiences.  I live in the county, and we often have animals "show up" in the area. And at times it is clear that they haven't been treated well.  I am so grateful to know that there is a humane society that will take them in and care for them.  We just aren't able to do this for all animals.
In a related experience, I was driving to work one day and there was a female dog running down the road that had clearly just had pups and she did not look good.  I stopped, got someone to help me put her in my car, and drove to the humane society with her.  Her paws were actually bleeding, and when I got there, they said the dog had been wandering for days and I suppose I was able to get her because she was tired.  I was so grateful they were there to care for her.
This doesn't mean they are perfect.  Our rescue African Grey parrot came to us because the humane society thought her growling meant she had to be put down because she was vicious!  They just don't get enough parrots to know how these exotic animals behave - (rural area) - they had the sense to take it to a vet to ask what to do... but clearly they have their limits. 
I often wonder how humane society workers do the work they do - many of the animals they see have not been treated well, and I suppose my experiences with parrot rescue have left me VERY cautious about placing them - and my guess is that humane societies see many animals that are lost, harmed, etc., because the pet has escaped enclosures, or owners have failed to contain their pets. 
And how is one to know that one person without a fence is in fact going to be the one who will be able to contain the pet?  And I wonder how I would feel if I approved an adoption and later learned that the animal had been hurt due to containment issues? 
I am so glad there are people with the courage to work in humane societies - I feel for animals that have been abandoned and abused, and at the same time feel I would just not be able to set the necessary boundary between the animals' pain and my own - hence - I donate funds rather than time to the shelter.  And I feel good about donating because of what they do to educate owners, because they have been there for animals in need of help. 
I sure hope is is OK for me to express my views here.  And that I have done so in a way that is respectful to differing views. I am sorry that you were denied the opportunity to adopt an animal you would give a good home to - and I just wanted to say that I can understand your view and understand theirs.  I hope my comments help you understand that their decision may have been based on the problems they often see.  Their model clearly is not perfect - and sometimes their rules are blindly applied - but overall, I am just so grateful for all they do. and I wanted to say that. 
Thanks for listening..