Shows who welcomed guests the day after Kimmel’s suspension — which also came two months after CBS said it would cancel Colbert’s show — varied widely. Fallon’s guests were actor Jude Law, journalist Tom Llamas and actor and singer Jonathan Groff — none of whom addressed Kimmel’s situation.

In 2004, Sumner Redstone was looking to add TV stations to the CBS portfolio and needed the approval of a then Republican-controlled Federal Communications Commission. At the time, President George W. Bush was facing a tough opponent in his bid for ...