Enough foreign countries were funding things by forging US dollars that a substantial fraction of the bills in circulation were not printed in the USA.
Of course the fiat system has its own dangers. And our current economic system not only has a fiat monetary system, it also has declared that the one zero-risk investment in the world is US debt. As I like to point out, if that assessment ever changes, the US government is suddenly going to find its debt a lot more expensive...
Cheers,
Ben