I never thought of the back being weaker by being pieced. I don't think that's a problem, and I piece most of my quilt backs to one degree or another. Here's one I pieced more than usual -
http://www.quiltingboard.com/picture...in-t23612.html
And once I pieced the back as if it were another top -
http://www.quiltingboard.com/picture...k-t216883.html.
I think piecing the back is a great way to use up scraps.