Rachel Nichols typically uses the opening moments of the ESPN basketball program, “The Jump,” to talk about the latest news in the NBA. On Monday, she used it to address a growing story that has her at the center.

In July of last year, Nichols was caught on video speaking to representatives of LeBron James about ESPN’s decision to have Maria Taylor host “NBA Countdown” during 2020’s NBA Finals. Her comments were recorded by a video camera she had left on and uploaded into ESPN’s system, where the footage was discovered and distributed by an employee. Nichols was frustrated that she hadn’t gotten the role, and suggested that ESPN’s interest in paying more attention to diversity was a factor in the decision.

Her comments leaked and have continued to generate disruption at the Disney-owned sports-media giant. In a story published Sunday, the New York Times reported that Taylor,...