Every macro textbook out there states that if a country has a Current Account deficit, it must have a surplus in the Financial account, but I have not heard a convincing explanation.

Imagine a country that imports something and does not export anything. Why is it that macro textbooks state that the only way for a country to pull that off is by borrowing from the country from which they import. Why? The company that did the importing need not have borrowed to buy the imports. In aggregate, imagine that a country is using its savings to finance the current account deficit so no borrowing takes place. What am I missing here?