The first thing I thought of is applique and paper piecing, neither always use pieces on the grain. I would think borders and binding should be on the grain in general, but there are exceptions to both. Since all pieces are either stitched down as in applique, or secured by quilting, I am not concerned by if all pieces are on the grain as there is no stress on each individual piece. I don't think the hard and fast rules of "on the grain" apply much to quilting.....clothes yes, quilts no. But then that is just me and my very humble opinion. If I am way out of line, please inform me why because I want to know.