"Food With Integrity" isn't a marketing slogan. It's not a product line of natural and organic foods.
It's a philosophy that we can always do better in terms of the food we buy. And when we say better, we mean better in every sense of the word- better tasting, coming from better sources, better for the environment, better for the animals, and better for the farmers who raise the animals and grow the produce.
The hallmarks of Food With Integrity include things like unprocessed, seasonal, family-farmed, sustainable, nutritious, naturally raised, added hormone free, organic, and artisanal.