Troy, "doubling wire drops three gauges" is an accepted principle of wire technology. You're correct that completely stripping the wires and binding the conductors together would accomplish this, but you're not grasping the fact that binding them together just at each end accomplishes the same electrical result. The conductors become a single wire(including the portions not in physical contact with each other)with a combined cross sectional area equal to the sum of the areas of the previously individual wires(i.e., double the area). Since the convention in designating wire gauges is that a wire with twice the cross sectional area of another is three gauges lower, the doubled wires likewise are likewise termed a wire three gauges lower. The electrical result of doubling the cross sectional area is halving the resistance.
Again, this is a well-established procedure.
