I do not believe that the price of bitcoin is dependent on the price of any fiat currency not even the US dollar. The price of bitcoin is only pegged to the USD because of its dominance in the market most likely because of the stock market.
I would agree that the price of bitcoin is not dependent on the price of any fiat currency, that being said most of the world financial transactions are made in dollars and Bitcoin in dollars are the cross people are watching agains their own local currency.
So when the dollar drops Bitcoin gets cheaper in lets say euro and investors buy Bitcoin because it's cheaper in their local currency, thus driving the price higher in dollar terms.