If they're buying the same amount elsewhere then the buy pressure equals the sell pressure, might make an arb opportunity across the currencies
The arb means you’re still suffering a price difference. You’re just paying “the market” to solve it for you.
Related. Not equal.
In reality markets aren't perfect, and also you'd have to take into account the benefit that doing things digitally is much faster, so it won't actually be equal. But in the magic world that economists live in it should be.