The genetics test you have linked shows the following: over 250 breeds. The problem is very likely in the methodology (way they try to figure out the breed). This is because all dogs, if size would not be a problem, can breed. It is still one species. Even a wolf can breed with, say a labradoodle, and produce fertile offspring (just not a good pets with that much wolf).
So, this company has taken at least 250 genetic samples from "pure breeds" and then tries to see if there are genetic differences between them. Of course there are. But those can be quite small: breeds are selected on mostly by two things: exterior and behaviour. Small you say? Yes: the amount of genes does not change, just the ones that get expressed: they are doing something with the dog. But they do not change the number of genes, or add a new functionality.
So, your lovely *Medium sized papillon had won a genetic lottery: some of its ancestry is a mix with papillon, but the papillon genes for exterior won out, except for size. Now, the other ancestry will have left its trace in the DNA of your dog, its that the company doing the testing did not test on those parts, or could not find them. But that does not exclude the possibility...
Without knowing the algorithm this company used we can only say that your lovely dog has a lot of genes from its papillon ancestry expressed. And that is about it.
But as your papillon is not within breed standards, in that way it will not be considered part of that breed. It also lacks the papers to show it's ancestry, the normal way of considering "pure" breed. And it seems that size is one thing that is does not varies much from its parents. It will be useful to talk to breeders of papillons about your dog.
As for "Wisdom Panel official certificate of pure bred-ness". Don't think that will hold with the kennel club or with the breeders association for papillons.
*Poodles use at least 3 sizes: Standard Poodle, Miniature Poodle and Toy Poodle. Normal papillon seems to be the size of Toy Poodles.
disclaimer: I am no breeder nor geneticist.