She can't take the dog. As she says, it's stealing and she could be prosecuted for a crime.
And rescue groups have a pretty extensive protocol for anyone turning their pet over to them to make sure the dog is legally theirs to place in a new home. They are just as careful about accepting a dog as they are about placing one. That's why it is never a good idea to adopt a dog or cat from a shelter to "save" it with the intention of turning it over to rescue. It doesn't work that way. The dog or cat might not be accepted, and you might end up with a dog you don't want or having to return it to the shelter.