Are you sure he didn't mean batting and not backing? There are many very nice washable wool battings on the market. I would be hesitant to use a wool backing for the reasons Tartan stated. Also it would be extremely cost prohibitive. Average price of wool fabric is in excess of $20 per yard (although it can be found cheaper on the net)
I can also confirm the scratchy. I used an old wool army blanket for batting on a quilt and even with 100% cotton fabric covering it, the scratchy still comes through. I can only use this quilt when it is layered on top of other quilts and blankets or have it hanging on a wall. Wool batting is not scratchy like a wool blanket or like regular woven wool fabric can be and it won't shrink or felt with washing.