That's not quite true. What all your sources say, is that it is influenced by chicken feed. Specifically "the amount and type of carotenoids the chicken consumes."
You can argue that it doesn't matter what chickens eat, and you could win. But I'd wager that to a great many people the quality of food does matter.
"Some studies have shown, however, that eggs from pasture-raised hens can have more omega-3s and vitamins but less cholesterol due to healthier, more natural feed."
You can argue that it doesn't matter what chickens eat, and you could win. But I'd wager that to a great many people the quality of food does matter.
There is the spurious matter of the nutritional quality of the eggs as discussed here http://www.thekitchn.com/what-does-egg-yolk-color-actually-m...
"Some studies have shown, however, that eggs from pasture-raised hens can have more omega-3s and vitamins but less cholesterol due to healthier, more natural feed."