When Donald Trump Jr. abruptly posted a series of private emails on Tuesday — revealing that he had agreed to a meeting last year to hear damaging information about Hillary Clinton proffered by an intermediary for the Russian government — he offered his 1.1 million Twitter followers a pre-emptive explanation.

He posted the emails, Donald Trump Jr. wrote, “in order to be totally transparent,” zeroing in on an idea that quickly gained traction among his family members and their supporters in the news media. Bill O’Reilly, the former Fox News anchor, called him “smart to release emails.” President Trump, in his own statement, said he applauded his son’s “transparency.”

The word seemed intended to make the younger Mr. Trump appear more than willing to release private communications to clear up confusion.

The reality was more complicated.

About an hour before Donald Trump Jr.’s tweets, The New York Times informed his representatives that it had reviewed the emails and was planning to publish them on its website. The Times, which since Saturday had published several articles about the meeting last year, asked if the younger Mr. Trump wanted to comment for the article.