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As long as they have the range to roam in, they can subsist on hand fed "vegetable waste." At the basic level, chickens are like us, in that they need a balance of elements in their diet: protein, carbohydrates, fats, vitamins and minerals in proper proportion. In the wild they eat seeds/grains, nuts, insects, grubs, microbial foods, worms, carrion and green feeds..... as long as it is there. They are actually omnivorous.
So, yeah, you can get them to survive on most anything. Personally, I've never been driven to feed them this way, i.e., solely from what they can scrounge and whatever scraps I can arrange. Few people do a critical analysis of their range, so they know little about what sorts of foods it provides over the course of the seasons. That said, I consider any birds I keep as my livestock, and I am their steward. I'll offer them the best I can arrange, first, and they can scrabble up what else comes.
I'm certain the chap was oversimplifying. Most likely he was spinning you with a little bit of 'New Age' marketing, probably assuming you were a "city slicker."
He's probably learned that most of his drive-up customers get excited about "all natural, free ranged, pro-biotic, vegetarian chickens"... no matter how ill defined that is.