Battery provides counterweight required to lift. Two primary factors determining effectiveness of counterweight are total weight + distance from fulcrum or tipping point, which is the front wheels (load wheels). Battery weight must meet minimum battery weight requirement listed on truck label, period. Anything less reduces the capacity, and as with any modification, it must be approved by the manufacturer. If approved, a new capacity label will be provided to replace the original label. When the truck specs call for "C" box, a heavier battery may be listed in order to fill up the box properly (I'm guessing), so the battery does not jump around in there during operation, which will create a rather unstable condition.

My advice: don't question the battery specs, get the right battery, move on. Otherwise, you may find yourself responsible for a tipped over Turret Truck.