They do cut things out at times. Which is also why they don't love stream it anymore. They needed to be able to cut out certain things. Though I don't know what their criteria is.
That’s not true. The reason they stopped live streaming is because sketchy channels were cutting clips mid stream and re-posting. Essentially pirating the content to make a bunch of cash before they had the opportunity to release the official clips.
Regardless of the reason, Rogan has told guests that they can cut out things if necessary since they don't stream live anymore.