Yes you are wrong.
Best L/D ratio is only a function of the airfoil! Best L/D ratio defines the best gradient. To achieve best L/D ratio a heavier a/c will need to fly at a higher speed. Ofcourse this higher speed comes with a higher ROD than with the lighter aircraft but the resulting gradient is identical. The heavier A/C will fly faster and hit the ground first, but at exactly the same spot as its lighter weight counterpart.
What happens with the extra energy of the heavier aircraft? Well the heavier aircraft will need more lift and this extra lift will give more induced drag, and also more parasite drag as a function of the increased speed.
The Lift/Drag curve for a heavier weight a/c moves with its best L/D point moving along from a line starting in the origin of the graph.
the QRH gives a glide ratio for green-dot at 2.5NM/1000ft. This equates to 400ft/NM. This is directly proportional to the L/D ratio of this airfoil at any weight in this specific config.
You will be telling me next that a heavy aircraft takes the same energy to climb to a particular altitude as a light one because L/D is only a factor of the aerofoil
This is were thrust comes into the equation.....
What we see on the line is that a lighter aircraft will descend steeper than a heavier one. This is because we don't fly the same L/D ratios. When flying 300knots in a 70t a/c we will have a better gradient than at 60t because at 70t and 300kt we will be closer to the green-dot (=best L/D) for that specific weight. Even ECON/managed descent speeds for different weights do not have the same L/D ratio. Unless they had the same factor over its respective green-dot.