I can remember my grandma using sheets for backing her quilts as a mater of money. But she always used up everything including my grandpa's clothes for quilting. If you are making your quilt to show then maybe I would not use sheets but for practical quilts I don't see why not. I have three quilts my grandma made in the 40's with sheets and clothes and they are so soft and snuggly and thats the way it should be....treasured.