Traditionally, when I hear about eating cheaply, I think "rice and beans". So I'm a little surprised to see those absent. Comments?
I don't think a $30/week grocery budget is unreasonable at all, with a bit of ingenuity (and, critically, proximity to the aforementioned vendors; food deserts turn this whole thing on its head).
On a per-calorie basis, almost all fresh fruits and vegetables are insanely expensive - someone on $30/week could perhaps afford an occasional banana.
Recently my local Trader Joe's was selling onions at $1.09 (or was it $1.19?) per onion. Per onion!
TLDR, heaven forbid you are rural poor.
He may not have many bean soup / bean salad / crockpot recipes.