Of course there are differences in where you are and what you have available.
That being said, since we don't buy any meat products or dairy, our situation is a bit different than most people's. However here in Indiana, the closest Whole Foods/TJ's is an hour away, so we mostly shop at Kroger. I plan our meals around what is in season and what is on sale, and I freeze everything I can when I can find a good price. I blanched asparagus this spring, froze peppers from my garden for cooking, etc. And my "garden" was a 6ft by 2ft plot of dirt and several containers, we don't have a huge amount of land anymore. Our coat closet doubles as a pantry for when we make the trip to WF/TJ's and stock up on shelf stable items.
Eating healthy can be more expensive, but it doesn't have to be as expensive as that study shows - if you're able to eat in-season.
We probably spend less than $100/week to feed both of us and our dogs, including toiletries and the occasional meal out. We used to spend a LOT more than that when we bought Mt Dew, Doritos, pizza, etc.