I agree with Aly- take the dog and find a good home for it! There is no way they will know for sure it was you, especially if you one day say "hey, where is your dog?"
About reporting them, I just think they will figure it out. Then what happens to the dog? What guarentee is there that the dog will find another good home? What if they are just contacted and told to stop neglecting/abusing their dog? I have heard that usually with a first offense, all that happens is a talking to, and then after that, there is no way you can take the dog, because they will know it's you.
And just because they are contacted, it does not mean they will change.

Go for it!