That means the whole time that Mr. Murdoch’s highly influential news organizations were covering Mr. Trump’s campaign and transition, their executive chairman was entangled in a financial arrangement of the most personal sort — tied to his children’s financial (very) well being — along with the president’s daughter.

Referring to her only as the president’s “daughter” fails to capture her true role. She is Mr. Trump’s most trusted confidante. And she is married to a key presidential adviser, Jared Kushner, who, as it happens, is so close with Mr. Murdoch that he even helped Mr. Murdoch set up his bachelor pad after his last divorce, The New Yorker reported.

The latest news about the Murdoch-Trump axis is acutely problematic for the leadership at The Wall Street Journal — owned by News Corp. — as it seeks to quell a rebellion by a group of staff members who believe that the paper has held them back from more aggressively covering Mr. Trump, they suspect, under pressure from Mr. Murdoch. (As Joe Pompeo of Politico first reported last week, a meeting to discuss their grievances is to take place at The Journal on Monday.)

But the relationship between the president and Mr. Murdoch has implications well beyond The Journal, given the global breadth of Mr. Murdoch’s media holdings, his history of putting them to use for political leaders who then help him with his own business needs and Mr. Trump’s own reactivity to the news media.

How it all affects the rest of us depends on how powerfully Mr. Murdoch’s news media properties swing behind the new presidential agenda and how much criticism of Mr. Trump they’ll abide from their journalists and commentators. And all of that could depend on what Mr. Murdoch wants from the administration, and how badly he wants it.