Flavio Briatore, the Italian entrepreneur behind the Billionaire nightclub chain — he is also a convicted card cheat, a businessman banned from Formula One races for life for race fixing and the father of Heidi Klum’s child — is now perhaps best known for starring in the Italian version of “The Apprentice.”

“There was only one person that I wanted, and that was Flavio,” Mr. Trump said in a promo for the Italian show. In another spot, the two men appear together at Trump Tower in Manhattan, firing each other.

In May 2016 Mr. Briatore boasted to La Stampa, a newspaper based in Turin, about his weekend with Mr. Trump at Fashion Week in Paris in the 1990s. “I think I’m the first to bring him to Europe,” he told the paper. La Repubblica, a daily newspaper in Rome, identified him as “Trump’s best Italian friend.”

But now Mr. Briatore, through a spokeswoman, said he had never seen Mr. Trump in Italy, that they just ran into each other in Paris and that their relationship essentially amounted to a publicity stunt.

By contrast, Mr. Papale’s loyalty has not wavered.

Mr. Papale walked to a table where he keeps his most prized possessions. There was a medal awarded to him by the Russian government. There, too, was a brochure for Trump Grande condominiums, a favorite destination of wealthy Russians in Sunny Isles Beach, Fla., and, because of his efforts, the twin city of Taormina.