The government having the authority to decide what content constitutes misinformation, and to censor content that it considers harmful is precisely what liberals criticize in China saying that makes Chinese system authoritarian.

Its what they say they're complaining about. But more practically, what they're complaining about is the inability to disseminate their own misinformation within a rival nation's borders. They do not have any interest in Chinese media inundating American media centers, as evidenced by the banning of Confucius Centers around American Universities and the closure of the Houston Consulate office, as well as the threatened state censorship of TikTok and Tencent inside the US.

The criticism ultimately boils down to the specific content of the message. Only "true" messages can be considered subject to censorship. Anything we flag as "false" is treated as a form of attack by a rival power or subversive fifth column, not a legitimate expression of speech.