Tearing a large backing makes sense because the backing needs to be larger than the quilt top anyway. Tearing does damage fibers at the torn area, but only for about 2 inches (with the most damage being in the inch closest to the tear). You typically want your backing at least 4 inches larger than the quilt top (or the 6 inches the OP mentioned), so the part of the backing that will actually be in the quilt will be undamaged.