They legally own it in the sense that they are the legally registered owners, currently.

They do not legally own it in the sense that the original owner will not be able to eventually recover it after the fraud is unravelled.

Your instinct that this is odd is correct. It is odd because it isn't actually true. The statement of a police officer made while standing on the street outside someone's house deciding whose story to believe is not the final legal verdict on this case.

Every story I have read about this before is the transaction(s) are reversed. I presume the owner opted for cash instead of the property back.