If CNN (or for that matter any alphabet network) wants to climb in bed with the Clinton campaign, that’s their business. They should probably stop pretending to report the news, but it’s their prerogative. They are privately owned entities and, therefore, free to do as they please.
PBS is a different story. The network is subsidized by the federal government (read: taxpayers) to the tune of 15% of its budget and is therefore beholden to its stakeholders, if not honor-bound to show impartiality in political matters.
That it does not is revealed in an October 2015 email from Clinton campaign Communications Director Jennifer Palmieri:
I’m confident that there is a simple, logical explanation for this, which Hillary Clinton will gladly share … once she is elected president.