Here is my perspective~this type of thing happens all the time with rehomes. People take in pets and then do not realize how much work they really require. She is young, works a lot and hasn't put the time into training him properly. The reason that she is giving you that he is not fully house trained is the #1 reason for getting rid of pets. It sounds like she is trying to get back some of the money that she put into his care and vetting. She had him neutered because either someone told her that this would stop his marking or it was suggested by her vet. So she tallied up all of the money that she had spent thinking this is what she wants back for him. She has probably read or been told that she needs to charge a rehoming fee for him and this is why she is asking $500 OBO. This happens ALL THE TIME even on YT. Go take a look at the For Sale Forum and there is someone who thinks they can resell a 4 yr old for $1,000. It's never going to happen. It doesn't matter how much you paid originally someone will NEVER be willing to pay anywhere near that amount of money.
So that being said,
I do not believe he is stolen. But she is being unrealistic in the amount of money she wants for a rehoming fee. Personally, saying that he is not "standard" because he has a tail means nothing to me and the price you are willing to pay. Whenever a dog (any dog) is out of puppyhood their value decreases and that is why there are so many in shelters.

What should matter more then anything is are YOU willing to do what it takes to train him? If the answer is yes then you need to move on to the next question about his price. In the Rescue and Rehome Forum the highest price that you can ask is $300 for rehoming. IMO I would only pay that amount for a rescue and not from a private seller from an adult Yorkie EVER.
I have been asked about this type of thing many times on YT from members that have been faced with this exact same thing so it is not unusual at all.

My suggestion would be to ask for all him records from his vet. Don't expect them since most time even in rescue we do not get vet papers. Offer her somewhere around $100 and expect a counter offer but personally I would not go much higher. Explain to her that in order to bring him home he will need to go to the vet to be treated for fleas for XXX amount of money and that you would be willing to give him a good home. She might take it but if not you need to be willing to just walk away. Good luck and let us know how it turns out.
*I guarantee there is no stolen dog conspiracy