Folks are like this all the time. I always say they think everyone is like THEM! That's why they don't trust folks. I give folks the benefit of the doubt. Besides they're there to help the animals not the people. Screw the people, take the animals. If folks WILL lie do you really want them having the animals? Some of these shelter people haven't got a lick a sense.
What ticks me off, is then they let folks adopt cats or dogs WITHOUT a guarantee they'll be spayed. I say connect the shelter to the vets office who will do the surgery and if they don't show up to have them fixed go to their house and take the animal back.
You've got to understand sure it will be hard in the beginning, but as time goes by cats and dogs will be come scarce and folks will pay if they really want one.