In January, six months before the blockbuster accusations became public, Shari Redstone phoned fellow directors on CBS Corp.’s board to ask about rumors that the company’s chief executive, Leslie Moonves, was about to have a #MeToo moment.

There was nothing to it, they assured Ms. Redstone, president of CBS’s controlling shareholder National Amusements Inc. She phoned Mr. Moonves, and he told her the same, according to people familiar with the matter. A source close to Mr. Moonves said Ms. Redstone never raised the allegations...