WASHINGTON—When Peter Navarro needed financing for a documentary film on the dangers to the U.S. of China’s trade policy, he sought out Nucor Corp., an American steel company.

Nucor made payments to fund the film through a San Diego nonprofit then led by a friend of Mr. Navarro. The arrangement was examined as part of a broader 2012 FBI investigation of the nonprofit’s finances, according to three former employees of the nonprofit. No charges were filed.

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