However, we must mention the following is possible:
All AKC breeders are on the honor system regarding the parents of a puppy. In other words, if a breeder owns 2 purebreds and the purebred dam accidentally mates with a stray dog, a breeder technically can tell the AKC that the purebred sire is the father and without DNA testing - which is voluntary on the breeder's behalf - the AKC will trust the breeder.
While the registration shows that the parents are AKC registered Pugs, there is a chance that somewhere in the lineage (perhaps 3, 4 or even 10 generations back) there is another breed in there... somewhere... If so, the gene for the long hair jumped many generations. Since the great-grandmother of this Pug is said to have had long hair, perhaps that dog's grandparent was a different breed or something to this effect.
Do, however, note
that a 4th or 5th generation mixed dog can be extremely
close to being a purebred. For example, if you had a Pug and Pomeranian mixed dog (50/50), that dog could have long hair of course. If you then bred that mixed dog to a purebred Pug, that 2nd generation dog would be 75/25. Wait for the pup to mature and then him/her to another purebred Pug and the resulting litter is then 93.75/6.25. Once again, and it is 96.875/3.125.
And in this example, a 5th generation dog that had long hair but looked like a Pug would be 96.875% Pug.