You are correct, to a certain degree. The thing is, think of the airplane as a teeter-totter. The heavy engine is on a short arm, balanced by a longer, lighter tail. If you build heavy, it's like putting heavy weights up and down both fulcrum arms. The plane gets heavy, but it doesn't necessarily balance any better. You might still need some weight to balance the engine. If you build light, but need a little weight at the back to balance the weight of the muffler, or a larger engine, the plane will still be lighter, and fly better, than if built heavy.

What we always try to avoid, if possible, is a plane that's heavy in the tail needing nose weight to balance. Because, with a shorter moment arm, it takes more weight at the nose to balance a heavy tail. I'd much rather have to put an ounce of lead in the tail of a plane than eight ounces on the nose!