False advertising, yes. The only recourse would be civil court, and even at that, without a contract stating that AKC papers will be provided, there isn't much to do about it.
Here is a quote from the AKC (found at
American Kennel Club - About Registration):
When you buy a dog represented as AKC registrable, you should receive an AKC Dog Registration Application form properly filled out by the seller. When you complete your portion and submit it with the proper fee, this form will enable you to register the dog. When the application has been processed, you will receive an AKC Registration Certificate.
Under AKC Rules, any person who sells dogs represented as AKC registrable, must maintain records that make it possible to give full identifying information with every dog delivered even though AKC "papers" are not yet available. Do not accept a promise of later identification. And Another (from Dogs Sold Without Papers): The buyer of an AKC-registrable dog should obtain the dog's AKC papers from the seller at the same time the dog is purchased. If a dog is delivered or sold with the understanding that AKC papers will not be furnished, the buyer should sign a statement agreeing to this condition. This agreement should be kept in the seller's records.
If a person acquires a dog without papers, with the explicit understanding that papers will be furnished for payment of an additional amount of money, the buyer has, in effect, forfeited any rights to the papers. If at some later date the buyer wants papers, the AKC can only advise going back to the seller to resolve the matter.