They care because it becomes a political disaster for America when an American corporation is enabling some kind of bribery scandal. This could easily lead to

They care because it becomes a political disaster for America when an American corporation is enabling some kind of bribery scandal. This could easily lead to american investment abroad being blocked, and generally tarnishing the image of America on the international stage. A lot of the American world order is based upon the perception that America are "good guys", allowing corruption to run rampant is very counter to that.