First, my food budget doesn't include restaurant meals; I've actually allocated that expense in the "entertainment" category (any luxury/excesses are in that category).
Second, we cook our meals and eat mostly rich dishes (a staple we grew up on) and we have lots of fresh fruits and veggie plants in our backyard (tomatoes, potatoes, apples, oranges, garlic, onion, etc.), so we save b/c we don't need most store bought fruits and veggies. I grew up poor, so I learned early on how to spend wisely (coupons are a must). Keep in mind that most Americans live on substantially less then we do, so when you ponder how anyone could have a food budget under $1k just think of the Walmart cashiers, the fast food workers, the gas station attendants, the retail clerks, etc.--I assure you they all live more frugally than I and many have larger families to feed.