Granny Quilter: I disagree with your quilt class instructor. I'm a judge and I don't judge the back other than if pieced it is well done and not crooked. I don't know everything, but I don't know of a single show that had criteria for the back. Some recent quilters do very fancy stuff on the back but that is irrevelent to the top.
So I think your quilt class instructor is giving a personal opinion. Perhaps there are local fairs that require this but not in my 100's of judging experience. We look at the back to see if the back stitching is well done and may say "how clever to piece the back" but that's it.