You are changing the prerequisites by adding a time dimension. Sure, over time the the exchange rates differ, thatâ(TM)s why we have FX traders. But if you take a snapshot in time, the example still holds.
Financial institutions get their exchange rates from one of two sources, Reuters or Bloomberg. Yes there are variances in their pricing, but this variance is so small, that for all intents and purposes, the example still holds. We can, as you would like, apply the real world on. Financial institutions put margins on the exchange rates, and this margin makes the variances between Reuters and Bloomberg completely inconsequential. When you purchase currency across institutions at the same time, you are riding the margins, but not the underlying exchange rate.