I've had both happen to me - the customer give me a too short backing, and I've loaded them the wrong way. Now I measure every top and every back that come into the studio. If the customer misjudged, I can call and have them fix it. To keep me from messing up ;-), I place a safety pin at the top of each layer. Then when I load I make sure the safety pinned edges are BOTH on the leaders (or BOTH not on the leaders if I'm loading the long way).
When I loaded the wrong way, I didn't take the quilt off the frame. I just unpinned the bottom edges, and I used a little rolling cart that I can just fit my sewing machine on. I sew a few inches, move the cart, sew a few inches, etc. to add a new piece to the bottom. Repin that edge and you're good to go!
Andi