I use sheets all the time as backings and I still don't understand why some people think that they can't be used for machine quilting. All of my machines from my Featherweight, Singer 201, Bernina 830 Record (vintage) and Juki TL98Q and Juki Exceed 600 have absolutely no problem stitching through a sheet. My quilting buddy has a long arm Gammil and she doesn't understand the hesitation with sheets either. We use sheets all of the time for our QOV and she does a pile of them for us with no complaints. I'm sure it could be a different story if you were trying to hand quilt through a tightly woven sheet. We have had this sheet discussion on this forum several times and we've also had it at my quilt guild many times. Some of my quilt buddies think I'm "swearing" when I use sheets and backing in the same sentence. With quilt fabric at $15 a metre in Canada, I am unlikely to change my opinion as I can often buy a King sized sheet for $10 (a second or one from the Clearance Centre for Sears and Bed and Beyond or Len's Mills or Giant Tiger). I suspect it's like a lot of other issues in quilting. Use the materials and methods that work for you.