I believe traditional American piecing simply means hand-pieced with a single strand of thread. I looked up the quilt on a blog, and the blogger said it meant it was not paper-pieced. It was also hand quilted.
http://linda-koshka2quilts.blogspot....irmingham.html
Here is another site that mentions each star piece was "fussy cut":
http://quiltfeather.blogspot.com/201...=1376235675805