I don't have any personal experience with tanks having issues with not being supported in the middle. I have, however, spent a lot of time reading through threads about DIY stands, and, for the most part, 4 feet is the longest people recommend having a stand without at least one center support (not all, but most). And, even at 4 feet, many designs have a center support. So, based on what I've read, I wouldn't build a stand for myself that was over 4 feet that did not have a center support.
And yes, I'd be at least as concerned as you are that I could see light under the center of the tank.