I think cloth shooting bags are quite likely. Made of pillow ticking, not so much. Ticking would have cost money, and would have been valuable for other uses, besides being too light for the job. And, doubling it would have just doubled the cost. I suspect existing light canvas bags may have been repurposed into a shooting bag. There is some evidence that the eared cloth hats seen in some early western artwork, might actually have been a decorated, recycled, surplus canvas bag that appeared to have ears because of the corners at the bottom of the bag.
Hungry Horse
My grandparents were just about as, errr... Appalachian... as you can get; given what life-lessons I learned from them, I'd say the above is dead center in the 10-ring.
Once they'd both passed, I spent some time restoring their home, to be put on the market: the front yard sprinkler systems, among a few other things, had a few leaks. Grandpa had patched the original galvanized sprinkler line in several places; I found more than a couple spots he'd used 3-4 different types an sizes of pipe, within less than a foot. He'd used whatever recycled chunks and pieces he had in the garage at the time, rather than spend a dollar or two on six inches of plastic pipe.
Now, to put this perspective: Grandpa's only son-in-law (my old Pop) owned a hardware store. Less than a mile from Grandpa's house. And Pop would happily have given Grandpa the needed repair parts... but Grandpa wasn't havin' any of
that, neither: those new stock parts could be
sold, to a customer, for good cash money ($.50 here, $1.00 there...); so, since he had some "perfectly good" pieces he'd "saved" (dug outa the ground somewheres, in case he ever needed them), he'd just use those.
I have no doubt in mind: a lot of those "Southern Mountain" bags were made outa just about whatever those folks happened to have alayin around the place... but only if it couldn't be put to a "better" use.