I think that anecdotal evidence is misconstrued.
Scratch grains are very low in protein (an essential element for ovulation). They are also missing some of the vitamins and minerals in chicken feed.
Layer feed is comprised of all the amino acids, vitamins, minerals, fats and energy in the proper ratio that over a century of research has shown chickens need.
Try feeding one flock scratch grains and another layer feed. Eventually, the scratch flock will cease laying completely.
While very important, there are many other variables that affect production other than just feed type.