No. If you earn more than the allowable amount for the Foreign Earned Income Exclusion (FEIE), you claim the Foreign Tax Credit instead. Under the FTC, you essentially pay the higher of the two tax rates. Except the accounting can get tricky if you have multiple sources of income that are taxed at different rates between the US and the foreign country.

For example, if you earn 200k in a foreign country and that country charges you 75k on 190k of that, and decides that 10k doesn't count for some reason. Suppose the US rates are such that you owe 60k on 190k, then the FTC erases that 60k. But you might still owe 3k on the remaining 10k that the foreign country ignored.