Donald Trump spends a lot of time watching a variety of Fox News shows. He and many Republicans in Congress and the White House also watch Fox News. That is because Fox News is the primary source of information to the Republican base. Many of Trump's tweets are taken from policy positions developed by Fox News shows. Fox News also provides many of the arguments that are used by Trump and Republican leaders to undermine the Mueller investigation and other sources of bad news for the Trump administration.
Ordinarily, governments provide their propaganda arms with the information that they want the world to consume. Fox News has achieved a position in which it creates the messaging that influences what government officials think.