A pedigree is only as good as the registry that maintains the stud books. If you can't be sure of your dog's pedigree then you may as well save a dog in need and adopt from Chihuahua Rescue or your local shelter than to pay the price for a puppy with a dubious pedigree source.

The American Kennel Club has aspired to maintain accurate stud books since its inception on September 17, 1884, in the City of Philadelphia. You can read more at AKC History

A number of dog pedigree registries have sprung up in the United States. Generally resulting from disagreements with the parent clubs that make up the AKC, and breeders who were not able to secure AKC registration for their puppies, these people created new dog pedigree registries and usually with less stringent scrutiny.

A registry that will accept a photo of your dog and hand you a certificate of pedigree isn't worth the paper it is written on. How will anyone know if all of the dog's in your Chihuahua's back ground were indeed purebred Chihuahuas themselves? 

It is only by careful maintenance of each generation of pedigrees that there is any degree of certainty. Now thanks to breakthroughs in DNA science, certainty of parentage is even more certain.