[Our media columnist examined the unlikely power of The National Enquirer in December.]

Mr. Trump and Mr. Pecker were longtime friends — but the relationship between the two was said to be frayed in recent months, when American Media’s leadership entered into a deal with federal prosecutors looking into the company’s role in the hush payments made during the 2016 presidential campaign. Mr. Pecker and his associates had helped orchestrate the deals involving two women who alleged past affairs with Mr. Trump in “catch and kill” deals: the former Playboy model Karen McDougal and the porn star Stormy Daniels.

After The Enquirer made his private life public, giving Twitter wags and late-night hosts the chance to weigh in on his high-flown texting style, Mr. Bezos sprang into action, starting his own investigation of the tabloid’s motives and how it had come to possess his texts to Ms. Sanchez.

The Amazon founder, who at last count was worth $136 billion, suggested that he would spare no expense in taking the fight to the tabloid publisher. Leading the investigation was Gavin de Becker, Mr. Bezos’ longtime security chief, whom Mr. Bezos said he had instructed “to proceed with whatever budget he needed to pursue the facts in this matter.”

It was a bold move for someone who has often tried to evade the spotlight, even amid the frequent insults hurled his way by Mr. Trump, who has labeled the newspaper that Mr. Bezos purchased in 2013 as “The Amazon Post” and recently called him “Jeff Bozo” in a tweet.

[Mr. de Becker has advised celebrities on threats for decades.]

Mr. de Becker confirmed to The Daily Beast on Jan. 31 that he was leading the investigation into the matter of how the Enquirer had obtained the text messages. Not long afterward, The Post prepared an article exploring competing theories about the motivation behind the publication of the tawdry tale.

American Media made the next move, offering Mr. Bezos an offer that it wrongly assumed he could not refuse. And if he did say no? A future issue of The Enquirer would make him very unhappy, with the selfies and more of the steamy texts it had apparently obtained.

“Of course I don’t want personal photos published, but I also won’t participate in their well-known practice of blackmail, political favors, political attacks and corruption,” Mr. Bezos wrote. “I prefer to stand up, roll this log over and see what crawls out.”