This is not correct, it is only practically true in trivial cases. Excess taxation is a very real pain point for Americans living overseas, never mind the other indefensible things the US government does to its expats like FATCA.
Many types of income cannot be offset nor or they covered by tax treaties. Every time there is an impedance mismatch between US tax code and foreign tax code, including basic things like classification of income, deductions, and exemptions, you can end up with liabilities in both countries. It is not uncommon to pay more taxes in aggregate as an expat than you would pay in either country separately.
The way the US government, and some State governments, treat American expats is quite fucked.