"Fox News can be a little squishy, as we've seen this week," Robinson said.

Last week, Murdoch's son, James, who reportedly wants to move Fox News even more to the establishment middle, criticized Trump's response to Charlottesville in an email that was supposedly meant to be sent to his friends.

"The presence of hate in our society was appallingly laid bare as we watched swastikas brandished on the streets of Charlottesville and acts of brutal terrorism and violence perpetrated by a racist mob," he wrote in a letter to his friends last week that various outlets all conveniently received at the same time. "I can't even believe I have to write this: standing up to Nazis is essential; there are no good Nazis. Or Klansmen, or terrorists. Democrats, Republicans, and others must all agree on this, and it compromises nothing for them to do so."