That's now cheating, it's just another way of binding. The purpose of binding is to hide the raw edges of the top, back and batting. I do this often on my "drag-a-bout" quilts. I am "one of those" whose backings are made to match the top in some was so this does look good. If I make an "heirloom" quilt or the back is very different from the front, I make a separate binding.
In my opinion, we often get caught up in the "rules" of quilting when in reality there are none. Remember where quilting came from and do it your way!! Have fun and don't stress.