I don't stich around the edge of quilts before sewing bindings on, but I also don't sew the binding on with a 1/4 inch seam. Instead, I take the 1/4 foot off and put the regular presser foot on. I just measured, and that means I am getting a 5/16 seam....slightly larger than 1/4 inch.
I also cut my binding at 2 1/2 inches, double fold, machine stitch on top and fold over to hand stitch the binding on the back.
This is the way the learn-to-quilt class I took 7 years ago taught me to do it. It works quite well.
Dina