Actually, it wasn't under ingredients, it's under the first section "Product Name." The "digests" are what we're referring to as "natural flavoring." I'm guess digest wouldn't sound to good on a bag of food so that use broader term. Natural flavoring is made from "animal digest." You can't possibly think that's the actual meat as how on earth would meat, preserved enough to have such shelf life, still possess an odor like that?
The below article is from the FDA discussing how kibble gets that "fish" flavor or whatever they advertise.
"With respect to flavors, pet foods often contain "digests," which are materials treated with heat, enzymes and/or acids to form concentrated natural flavors. Only a small amount of a "chicken digest" is needed to produce a "Chicken Flavored Cat Food," even though no actual chicken is added to the food. Stocks or broths are also occasionally added. Whey is often used to add a milk flavor. Often labels will bear a claim of "no artificial flavors." Actually, artificial flavors are rarely used in pet foods. The major exception to that would be artificial smoke or bacon flavors, which are added to some treats."
I went to BB website and clicked on their fish/sweet potato food and looked at the ingredients and right away I saw "Natural Fish Flavoring." So you do know it's fish, but you can tell that from that food based on the fish smell anyway. But you have no idea what natural fish flavoring entails. Sure it could be boiled down fish broth... but what kind of chemicals are in to preserve that? Also makes me uncomfortable, not as much with fish, but they can use 4D animals to boil down and make such broth.