Some of it is misleading. Beans and nuts, especially when combined with grains, are also affordable protein sources, probably THE most affordable sources.
Until factory farming post WW2, chicken was one of the most expensive meats, thus recipes for 'city chicken' made from veal, which was cheaper and far more plentiful. Chickens have to be carefully cared for and fed. They were generally kept by farmers for the eggs, and only killed and eaten when old and beyond laying, many medieval peasants did not have the resources to run their own chicken coops. Meanwhile, the medieval peasant had streams and oceans full of fish, forests full of game, and plenty of assorted rodents readily available. (we have Roman recipes for mice)
But, the medieval diet for rich and poor alike was governed by the principle of balancing 'humors' and most often consisted of grain-based gruel with various flavorings depending upon a person's health. They boiled everything into these gruels, including vegetables like lettuce, eating very little, if anything, raw. They cooked in pots over the home hearth, home ovens were rare signs of wealth. (The home stove and oven are an invention of the 1800s) An average peasant family took their raw loaves to the village baker to be baked for a fee. That baker would cook other dishes as well, but, doing so cost a family dearly. (boulangere potatoes evolved as one of those type dishes, obviously post Columbus)
I am not a fan of Mr. Ruhlman, btw. My 'last straw' with him was his blog post, since deleted, where he quite seriously quoted Eric Ripert stating that it is a well known fact that women are inferior as chefs because it is impossible for a menstruating woman to make mayonnaise without it breaking. He only withdrew the post a week later following video demonstrations by several female bloggers (one wasn't enough to convince him) creating perfect, unbroken mayonnaises while 'Aunt Flo' was visiting.