Sure there are problems, but the mainstream news has proven to be fairly reliable over the years, most of the time. You would not believe rumours on social media that Bush was responsible for 9/11 because of that.
The problem for China is that once they cripple official sources of news, rumours become much, much more credible. Denials or ignoring of them by state media is meaningless. They potentially make the problem much worse.
Except that most Chinese, even more so than Americans, are sheep. With a few wolves among them.