Whole plant foods are the cheapest calories in the store
What costs money is protein, packaging, and someone else doing the cooking. This site skips all three. Every recipe is built from whole plant foods with no added oil, no added sugar, no refined flour, and little added salt.
The cheapest diet is not automatically the healthiest. The best evidence puts the healthiest eating patterns at roughly a dollar and a half a day more than the least healthy ones, with most of that gap in meat and protein (Rao et al., BMJ Open 2013, doi:10.1136/bmjopen-2013-004277). The defensible claim, and the one this site makes, is narrower: pound for pound and calorie for calorie, whole plant staples are the least expensive food in the store.