An accounting identity is true by definition. What countries report as their trade statistics are only the measured values for these trade balances, not the true values. Statisticians and accountants attempt to measure international transactions as accurately as possible. However, a quick look at any country's balance of payments statistics reveals that the balance on current account plus the balance on capital account rarely, if ever, sums to zero. The reason is not that the identity is wrong, but rather, that all of the international transactions on the balance of payments are not accounted for properly.
Measurement errors are common.
These errors are reported in a line in the balance of payments labeled, statistical discrepancy. The statistical discrepancy represents the amount that must be added or subtracted to force the measured current account balance and the measured capital account balance to zero. This is an important point because it is often incorrectly perceived that a trade deficit, for example, implies that unfair trade is taking place. After all, the logic goes, when imports exceed exports, foreigners are not buying as many of our goods as we are buying of theirs. That's unequal exchange and that's unfair.