Emphasis on “was.”

In recent weeks, Mr. Pecker has emerged as a cooperating witness in the federal investigation that prosecutors in the Southern District of New York are pursuing into the schemes to pay six figures to Ms. McDougal and Stormy Daniels, another woman whose story of an affair with Mr. Trump was buried by the company.

In the Sunday-night tweet, Mr. Trump was effectively vouching for the credibility of Mr. Pecker and his newspaper — whose name in the Trump era hasn’t exactly been equated with accuracy. To wit, Hillary Clinton is still alive, proving that The Enquirer’s campaign-year reports of her imminent death were a bit of an exaggeration.

Mr. Pecker’s word is of high value to prosecutors — and highly dangerous to Mr. Trump.

Mr. Pecker provided vital corroboration for the story told by Mr. Trump’s former lawyer and fixer, Michael Cohen, when he pleaded guilty last year to arranging the payments to Ms. Daniels and Ms. McDougal.

Mr. Cohen said he had arranged them with the full knowledge that they were equivalent to illegal campaign disbursements, because they were intended to help Mr. Trump win the election. He also said he had made the payments at Mr. Trump’s direction, essentially accusing his former boss of being the driving force behind the whole thing.

In December, Mr. Cohen was sentenced to three years in prison on those charges and others. In a court filing provided ahead of that sentencing, the New York prosecutors disclosed the extent of American Media’s cooperation. The company’s willingness to help is why there have been no charges against those involved with the running of the tabloid, prosecutors said.

The cooperation of American Media officers was highly significant, because Mr. Cohen made for a flawed witness. His long track record of lies meant anything he said to law enforcement officials would require corroboration, if it were to be of any real value.

After months of public denials that the payment to Ms. McDougal had been coordinated with Mr. Trump or Mr. Cohen, American Media flipped the script, telling prosecutors that it had coughed up the cash “in cooperation, consultation and concert with, and at the request and suggestion of, one or more members or agents of” Mr. Trump’s campaign. The publisher also explained why it had done so — so that Ms. McDougal “did not publicize damaging allegations” and “thereby influence that election.”