You're right, Leenia; I misused the term "batting." Your distinction between "batting" and "stuffing" is correct.

Maybe I was misled by this old nursery rhyme--

Pretty Kitty Creighton had a cotton batten cat.
The cotton batten kitten once was bitten by a rat.
The kitten that was bitten had a button for an eye,
And the biting of the button made the cotton batten fly.

--which gives the impression batting is synonymous with stuffing, since it describes a stuffed toy.

By the way, I found that rhyme using Google books, and then modified it to make it closer to the way I think my mom recited it. I can't remember what name she used; I don't think it was "Creighton." "Kelly" maybe? I was surprised that I couldn't find it in a book older than 2006. I definitely remember hearing some version of it when I was quite young, probably in the early 1950s.

By the way, 12-stringer, I have listened again to the song and I agree with your corrections. the term "batting."