Late on a Monday afternoon in June, members of CNN’s elite investigations team were summoned to a fourth-floor room in the network’s glassy headquarters in Midtown Manhattan.

A top CNN executive, Terence Burke, had startling news: three of their colleagues, including the team’s executive editor, were leaving the network in the wake of a retracted article about Russia and a close ally of President Trump. Effective immediately, Mr. Burke said, the team would stop publishing stories while managers reviewed what had gone wrong.