A security contractor lawfully could silence a worker’s union representatives during an investigative interview and control when they could speak, a divided National Labor Relations Board ruled.

Two of the NLRB’s Republican members said in a March 8 decision that the PAE Applied Technologies official who conducted the interview quieted everyone—both management and union officials alike—in a seven-person meeting that had become unruly. The worker had adequate assistance even though the union representatives weren’t allowed to participate while he prepared a written statement about the incident under investigation or during a question-and-answer session, according to the ruling.

The company’s steps...