I think you've answered your own question....Surely it is passenger's journey origin that determines whether the upgrade is available, not the origin or intermediate calling points of the train? The T&Cs read:
5.5. Gold Card First Supplement tickets are not valid for travel on Mondays to Fridays between 1600 and 1900 inclusive for journeys departing from any London terminal station, or any intermediate station between London and Clapham Junction inclusive.
The last part would make no sense if it was the train's origin that mattered - no trains originate between London and Clapham Junction.