Three days after Tokyo-based trader Tom Hayes was fired by Citigroup Inc. for trying to manipulate benchmark rates, he shot off a letter to one of the bank's human-resources executives.

"My actions were entirely consistent with those of others at senior levels" in Citigroup Japan, he wrote on Sept. 9, 2010, and "the senior management at [Citigroup Japan] were aware of my actions."

Regulators...