Stretching the backing just taut, but not tightly, keeps the backing from puckering while quilting. If you pull it too tightly, that will cause wrinkles and puckers too.
Yes, starting at the center and working outwards does keep the sandwich more flat and straight, but the actual act of stitching it all together, does make the sandwich shrink in a bit. For some reason, the backing tends to shrink/pull in more during quilting than the top does.