"Pure" in the chicken world is far, far different than "pure" in the horse world, where pedigree is the whole focus.
In chickens, it does not matter hardly an speck. The entire beginning and ending, Alpha to Omega is the physical appearance of the bird. Birds are not kept by lineage or pedigree. It's about what the bird looks like. How good are its features.
If a bird was supposedly from great birds but now any chick that grows out and has faults all over the place? Faults and DQ's from the Standard of the breed? It's nothing. Nada. Either a pet, an egg layer or a cull. That's it. It just cannot be shown. End of story.
This is what "pure" means in the chicken world. Pure means bred to the Standard, exhibiting the traits of the Standard. Without manifesting those high quality features? Sorry. It just isn't a bird said to be a good example.
Don't be discouraged, as it is very challenging to breed to quality birds. The vast majority of bird fall quite below breed standards level.