Your logic is cute but flawed. Gold has been rising against all major currencies and by roughly the same amount. I know you next point will be that gold is showing how all fiat currecies are bs.

But does it really defeat the hypothesis? I'm not sure. It seems to me that supposing buyers who are willing to throw dollars around as if they were worthless and thus drive up the dollar price of gold, arbitrage will spread the price increase to other currencies, especially if the dollar retains some element of a reserve currency. With a minor currency it would be more likely that the effect would be isolated to that currency.