Sorry to bump an old thread but I'm having the identical issue as the OP. The car runs/starts fine and all electronics are fine. I am also getting this charging system failure issue on my 2005 Grand Prix GT. I've cleaned my battery terminals, checked voltage at battery and alternator, checked OBD II voltage and all checks out fine when off or even on a load. All of the local auto part stores say everything is fine with my battery and alternator. The battery was replaced a few years ago and the alternator is original.
Just as the OP said, when I unplug this mystery black wire with a white line on it that comes right from the ground wires on the battery terminal, the voltage will read correct on the DIC but I get a service vehicle soon message. When I plug it back in, the voltage on the DIC shoots up to ~18-25 volts and says charging system failure. When checked with my DMM, it shows a proper 12.8-14.5 volts.
I've been troubleshooting this for 2 weeks and want to figure it out. I am beyond stumped and want to get this taken care of. Any help or advice is appreciated!