AFAIK, the censorship is driven by the fear that the western media's intention is to subvert the CCP ruling. Fake news were never a problem. Unless the fake news has the same effect. But in that case, it's not difficult to disapprove the claim anyway.

China's Internet is full of junk and fake information. A while ago a poor young man's family spent their life's saving on hospital treatment that in reality does not help anything. Their belief comes from a seemingly legitimate source on Baidu Tieba. And just a few days ago, a patient believed that a doctor maliciously ignore his request to treat his daughter according to the fake "treatment" from some online search results. And stubbed the doctor 9 times, one of them pierced the doctor's heart.

Such stuff are routinely ignored, why? Because they do not pose a threat to the government's ruling. Instead, they actually reinforce the fact that government control over media is needed, which obviously is a vote to their continued ruling.

Another joke I learned recently perfectly explains this fact: In a community there is an abandoned car. The residents repeatedly ask the community manager to move it and no one did anything. Then one day someone painted "democracy, freedom" on the car, then the car disappeared next day...