That ticking noise that begins every 60 Minutes segment? Turns out that’s not a stopwatch. It’s a time bomb.

At least that’s how it’s sounding lately, like the illustrious citadel of American broadcast journalism is on the brink of blowing up. Last night, in the latest shudder suggesting an imminent explosion, correspondent Scott Pelley ended the show with a “Last Minute” segment that all but declared open rebellion against 60 Minutes’ corporate overlords at Paramount and raised a fist in solidarity with longtime executive producer Bill Owens, who just days earlier had bolted CBS in protest over what he called editorial meddling by management.

“No one here is happy about it,” Pelley informed viewers, perched on a stool before a backdrop of the program’s iconic ticking timepiece. “But in resigning, Bill proved one thing — he was the right person to lead 60 Minutes all along.”

What...