She's wrong. A dog is "property" in the eyes of the law. Make sure you have all your ducks in a row with regard to receipts, etc. showing that it was you who purchased the dog, and that it was you who paid for things such as food, grooming, etc. You'd be surprised how often a dating couple who shares a dog goes to court over the dog after they break up. If what you're saying is true, you should be in the clear. Good luck.