I think you are just quoting something you heard somewhere and have no real knowlege of. There are so many hundreds of breeds that are shown and thousands of different breeders who show, that are breeding for different ideals. It would do a show breeder no good if they breed all the production, vigor and fertility out of their birds. How would they keep their lines perpetuating.
I personally have show birds and do show my breeding birds. Last fall my two most prolific and strong roosters were shown because they represented the best of the araucana that I have. Same goes for the hens. I breed the best hens I have to the best roosters, not just for looks but for egg laying year round and to be a dual purpose meet bird. If I didn't breed my best and healthiest together I would never and I mean never get a bird that was show quality. My hens are used as broodies also when they want to hatch eggs. That is what the Standard of Perfection for my breed calls for. A dual purpose breed, Not a pale wasted bird that doesn't lay eggs or can't feed your family if need be.
I have found Personally that my pure bred show birds are laying much longer and more reliably then any hatchery bird I have ever bought no matter the breed and I have about 10 different hatchery breeds represented in my table egg laying flock along with some araucana that are not correct to breed type in all respects.
I don't advocate that everyone run out and buy a show bird or even a bird from show quality stock for just some back yard eggs. Why spend the money. However if you are going to show or breed your birds, a breeder is where you really should start.
Lanae