“I was with one of the greatest companies in the world. The chief executive officer. Very short while ago. And it really affects him,” Trump said at a July 31 campaign rally in Tampa, referring to his controversial use of tariffs. “He said ‘You know what, this does affect our company. But, Mr. President, keep going. You’re doing the right thing.”’

Trump didn’t identify his supporter, and the White House won’t say who it is. Trade groups representing the largest U.S. businesses and CEOs have almost universally opposed Trump’s disruptive approach to trade. But the person fits a model: an anonymous figure — important and powerful — who invariably supports the president’s position, according to Trump himself.

They are fixtures of Trump’s speeches, defying conventional wisdom and popping up to back the president on issues including prison reform and immigration, in addition to trade. In some cases Trump’s accounts are rebutted by the people he seems to describe. Key details change when he repeats the stories.