As part of his work for the company, Mr. Davis said, he met with journalists from The Associated Press to “let them judge whether the reason not to publish” a particular article about Mr. Trump was part of a so-called catch-and-kill playbook to protect him.

“All I did was pass along the documents that the editor said was the reason why he didn’t print the story — the lack of credibility of the source,” Mr. Davis said. “Never was there a sentence uttered that you should kill this story. That’s what I do: facts, facts, facts.”

Even before he took on Mr. Cohen’s case, Mr. Davis’s flood-the-zone model of representation had become especially common in the Trump administration’s recent months, touching a series of Trump-branded scandals. Lawyers like Rudolph W. Giuliani (working for the president) and Michael Avenatti (working for Stephanie Clifford, a pornographic film actress who also received a hush payment from Mr. Cohen) have often seemed to understand their roles more as ubiquitous advocates and jack-of-all-problems defenders than simply traditional legal minds, much as Mr. Cohen viewed himself, until recently, in service of Mr. Trump.

Mr. Davis said he would not do anything to undercut Mr. Cohen’s position with prosecutors. And he pledged to step back, for now, from public remarks about the recording.

“I don’t need to speak any further or go on any more shows,” Mr. Davis said. “The tape speaks much better than I do.”

But then he spoke further. He offered Mr. Trump and his team unsolicited crisis management counsel from his literary canon. “The mantra — tell it early, tell it all, tell it yourself — the ‘it’ is the truth,” he said. “Now what did Rudy Giuliani do? He and Trump walked into the trap thinking they could get away with lying.”