One aspect of American exceptionalism is undoubtedly true. American policymakers believe that they have been anointed by heaven to rule the world. Just as God cares if a sparrow falls to earth, U.S. officials believe anything anyone does anywhere on the planet is a matter of Washington's concern. That is reflected in a foreign policy which essentially has turned the Monroe Doctrine into a global strategy: the US, and only the US, is entitled to intervene everywhere on earth.
Admittedly, the policy is not entirely consistent, with Uncle Sam sometimes implicitly delegating its authority. For instance, Washington cares little if, say, France sends its troops to Francophone Africa. Libya became a military mishmash involving several European and Middle Eastern allies, while Washington stuck with diplomacy. American officials did not object when Saudi Arabia used its military to bolster Bahrain's minority Sunni monarchy, crushing largely Shia pro-democracy protests; worse, the US actively aided Riyadh's murderous invasion of Yemen.