It is surprising how often people who dump animals get caught. There are a lot of people out there who care about animals. They notice things, and call people. There are sometimes little clues that you wouldn't think of, like addresses on cardboard boxes. There are fortuitous accidents, like the little girl who happened to recognize the kittens.
Neighbors notice that a whole litter of puppies suddenly was no longer there.
Dumping a litter of kittens at a veterinary clinic on a Sunday afternoon may seem like an easy solution to a problem, but it is not much different than dumping them in the middle of a high traffic bridge in downtown Seattle. Having animals is a responsibility. The majority of pet owners are responsible about taking care of their animals. About thirty percent of the tax payers don't own any pets. Responsible pet owners, and people who don't own pets, have to pay the costs of the irresponsible behavior of pet owners like the ones who dumped those kittens.