Once you are into providing chickens a grain based formulation that is optimized for only growth / egg production, you are providing a diet that is lean with respect to nutrients that impart qualities on eggs we associate with free-range foraging. Having birds out getting some greens can off set some of that diluted (from formulated diet) carotenoid intake. The greens as far as I know do not offset / improve uptake efficiency, rather they simply provide more for the bird to extract from. The supplements are simply a carotenoid rich / dense component of the diet. Actual greens my bird consumed are acquired largely though free-range foraging although confined birds can also get them through consuming sprouted grains. I have been using the ground pepper, paprika in particular, because it is easy to work with. I free-range many of my birds most of the year but now essentially all are confined which is the reason in the interest in the supplements.