Legally it does. If the dog is in your name with the Kennel Club, without any other proof (ie, if you'd sold the dog on, you can take that person to court and get your dog back as though they'd stolen it if you didn't sign a contract of sale.) you could easily get the dog back.

Its no very moral, but it still happens. KC papers are legal documents of sale in a court's eyes. You can only do a transfer of ownership through the KC with a KC dog and protect yourself and the new owner. This is why it is hugely important to get the history of any potential dog you are going to purchase.

This scam is becoming more and more huge, especially, I've seen in beagles.