I've heard a lot of people say this, but really it depends on the nature of your lower back problems. I've got three formerly herniated now bulging lumbar discs and have fought pain for years. My sports medicine/orthopedic surgeon recenlty recommended going for a much more upright position (switching from drops to risers and a taller stem) in order to reduce the angle on the lower back and keep it as arched (backwards) as possible. This has helped me quite a bit. I would agree that tailbone problems are another issue and would probably be better served by a more forward position with more weight on the bars. However, weight distribution for lower back issues may not be as important as reducing the angle between the legs and back. For example, standing is generally much easier on lumbar herniated discs than sitting in a chair, due to the leg position.

As for this thread, I'd really suggest seeking out an orthopedic surgeon or sports medicine doctor who is also a cycling enthusiast to talk through the problem if you continue to experience pain while riding.