Mivey, this is not true, nor is it relevant to the point being made. The point being made is that the voltage drop along the circuit does not cause the current to move in the circuit, but that current moving through the circuit causes the voltage drop.If you want the current from the rest of the circuit to flow through the wire in question, you must add enough additional potential force to overcome the wire resistance or some of the current is going to flow through a different channel.
All of the current from the "rest of the circuit" will flow through the wire in question without adding any additional force. The force that moves the current in the circuit is the potential source (such as the battery.)
If I connect a 12v battery to a 12 ohm resistor with "superconductors," 1 Amp will flow from the battery, through the super conductors and the resistor. There will be a 12 volt drop across the resistor, and 0 volt drop along each conductor. If I then replace the "superconductors" with "real" conductors that each add 0.5 ohms resistance to the circuit, 0.923 Amps will flow through the circuit. There will be a 0.0462 Volt drop along each of the conductors and a 11.076 volt drop across the resistor.
Current is flowing over the wire in question, but I have not added any additional potential to the circuit (and none of the current is flowing through any different channel.) So your first statement is wrong.
This statement is true, if we want the "same current" to flow through the circuit, but it is not "necessary" to add potential to CAUSE current to flow the circuit. Consider a 120V circuit with 1200 watt of incandescent lighting on it. We know that there will be a voltage drop on the circuit conductors feeding the lighting. In an ideal world, 1200 watt on a 120v circuit would create a 10 Amp current, but lets assume the circuit conductors add 0.25 ohms each. The current flowing the the circuit would the be 9.6 amps and my 1200 watts of light only output 1106 watts. But in this real world case, I'm not going to retap my transformer to increase the voltage to make sure I get 10 Amps, and therefore, 1200 Watts out of the circuit.If it takes 40 volts to push 10 amps of current through a circuit with superconductor wire, you are going to have to add more voltage force to push the same circuit current through a wire with some resistance.