Brownish chickens lay brown eggs, white chickens lay white eggs. Worked on my cousin's farm in Lost Nation, IA every summer for years. Seen 'em laying eggs real time!
Many a bird's nest in the trees when I was growing up and climbed trees had blue eggs in the nest. I think they were robin's nests. We had a wren house, cute little birds, but never looked inside to see what color their eggs were. They were a bit skittish, but they returned every year to that bird house attached to the clothes pole. Then one summer, none showed up and we always wondered what happened, did the bird get et, or died of old age or ?