The CG is where the plane balances, not some point picked by the designer of the plane. When you see the "CG" marked on plans or listed in the instructions, that's not the CG location, that's where they want you to put the CG. Just as a picture of the engine isn't the engine, it's where they want you to mount the engine.

A plane is tail heavy when the CG is too far back, nose heavy when the CG is too far forward.

"too far" is the tricky part. To far from what? It doesn't depend on what a designer put on the planes, it depends on the configuration of the plane, the aerodynamic forces that affect the stability of an airplane.