That may be true for where you live. You may have 3 or 4 different supermarket to shop at, you may also have Walmart or a Super Target. But in most poorer neighborhoods, they are lucky if there is one supermarket. And they don't double coupons, have loss leaders, etc. It's harder to find bargains under those conditions.
You are very smart to point this out. I have received actual training on poverty and people who live in poverty. One thing that really stuck in my mind was when I learned about how difficult it is in urban areas (especially inner city areas) to buy affordable food. In the suburbs, we have big box stores we can go to to get lower priced food and we have lots of variety. In some areas of this country, people are limited to bus transportation, or their own two feet, and often purchase their food at gas stations, or small shops in the inner city where the cost of food is significantly higher. They also purchase smaller quantities of food, so they can schlep it on the bus or walk home with it. They have eroded purchasing power as a result.