I'm 99.9999% sure that wire they have you cutting is connected to the battery or somewhere close to it and is connected to the regulator so it senses the voltage at the battery.
The modification has the wiring modified so the regulator senses the voltage at the output terminal of the alternator.
Why was it done that way from the factory? The wire between the output terminal of the alternator and the battery has voltage drop depending on the amount of current running through it. Sensing the voltage at the battery allows the alternator to compensate for this voltage drop.
It might be worth the effort to run a new wire from the battery back to the regulator (the 3-terminal connector). Or at least disconnecting the old wire so it doesn't short out.
