Some economists believe that the balance of payments is what determines currency exchange rates. In fact, exchange rates are always about the purchasing power of some currencies relative to others.
I often point out that I'm not a macro guy. Sometimes, I'm surprised to learn about the weird misconceptions they have. This is one such case.
Money supply (fiat currency supply, if you like) is obviously determined by central banks and their affiliated fractional reserve banking systems. Money demand, as the article states, is determined by purchasing power and purchasing power is about the productivity of the economy that's using that money. Those forces are going to determine exchange rates. Balance of payments just seems like a bit of accounting that happens after all the real economic activity sorts itself out.