I really respect the work the animal rescuers do, and have helped before in very minor ways, but from the outside, I do agree it can seem a little odd at times.
They don't want a tortured/neglected animal to end up in the same/worse situation.
You spent the time to seek out a shelter rather than a puppy mill...it would seem you have a desire to help the pet rather than abuse it.
My wife wanted a cat. We went to a rescue agency. We were on a rather large lot (8 acres), had a nice size house (3600 sqft), had a barn, and wanted a tough, older cat to work with...maybe a mouser.
My wife handled several cats and found one missing most of its fur and a glare to make you want to cry that had been pulled off the operating table where it was being put to sleep. My wife picked it up out of the cage, and it immediately clawed her face...blood was dripping down onto her shirt and on the floor. My wife held on with no panic and put it back in the cage. They were in a panic, but that is the cat my wife wanted.
There were two visits to the house before they were sure we could handle a cat....
....years go by....
The cat sucks as a mouser and rarely goes outside, but all the hair is grown back. She is a beautiful black cat, healthier than ever before, and a happy, gentle part of the family. I wouldn't trade that cat for anything.