This is correct. Not only are grocery store profit margins razor thin in a general sense, they're thinnest for packaged food found on the shelves in the middle of the store. The biggest margins are in seafood, meat counter, bakery, and produce—the ones more privileged people frequent more often, and poor people less. If the store is in a zip code where poverty is rampant, packaged, canned, and boxed food starts looking a lot like a cost center from a business perspective.

This isn't directly related to shoplifting and theft since the high priced items are usually behind the counter, but if you are a grocery chain with hundreds of stores the poorly performing ones are always going to be closed first. And those are almost always in urban, crime-ridden areas.

[Source: worked as a supermarket cashier as a teenager.]