The only thing I can think of is the maker intended to make a summer quilt with those pinwheel blocks without batting and only an unbleached muslin back. (I think you meant unbleached muslin, not unbleached calico, right?) Maybe she intended the straight stitching down the center to be the "quilting" and intended to join the blocks quilt-as-you-go style.
And I don't see how the 5" blocks could possibly be part of the same quilt.