Wow, what a story! These are just MY thoughts. First red flag for me is that the dog didn't even recognize her. Second, if the police officer is saying that you don't have to give in to her demands but if you don't she could pursue you legally, doesn't sound like she has the funds to do that, nor do I think she has the rationale to do that. I would think that if she doesn't pursue legal action and keeps calling and emailing you, which I hope you're keeping copies of, that you could turn around and have her charged with harassment. JMO.
P.S. I hope you get to keep the dog, it sounds like it would have a great forever home.