The Chinese government has become extremely effective in controlling what the country’s 1.4 billion people think and talk about.

But influencing the rest of the world is a different matter, as Peng Shuai has aptly demonstrated.

Chinese state media and its journalists have offered one piece of evidence after another to prove the star Chinese tennis player was safe and sound despite her public accusation of sexual assault against a powerful former vice premier.

One Beijing-controlled outlet claimed it obtained an email she wrote in which she denied the accusations. Another offered up a video of Ms. Peng at a dinner, in which she and her companions rather conspicuously discussed the date to prove that it was recorded this past weekend.

The international outcry grew only louder. Instead of persuading the world, China’s ham-handed response has become a textbook example of its inability to communicate with an audience that it can’t control through censorship and coercion.

The ruling Communist Party communicates through one-way, top-down messaging. It seems to have a hard time understanding that persuasive narratives must be backed by facts and verified by credible, independent sources.

In its official comments, China’s foreign ministry has mostly dodged questions about Ms. Peng, claiming first to be unaware of the matter, then that the topic fell outside its purview. On Tuesday, Zhao Lijian, a spokesman, leaned on a familiar tactic: questioning the motives behind the coverage of Ms. Peng’s allegations. “I hope certain people will stop malicious hype, not to mention to politicize it,” he told reporters.

China has grown more sophisticated in recent years at using the power of the internet to advance a more positive, less critical narrative — an effort that appears to work from time to time. But at its heart, China’s propaganda machine still believes the best way to make problems disappear is to shout down the other side. It can also threaten to close off access to its vast market and booming economy to silence companies and governments that don’t buy their line.

“Messages like these are meant as a demonstration of power: ‘We are telling you that she is fine, and who are you to say otherwise?’” Mareike Ohlberg, a fellow at the German Marshall Fund, a Berlin research institute, wrote on Twitter. “It’s not meant to convince people but to intimidate and demonstrate the power of the state.”

China has a history of less-than-believable testimonials. A jailed prominent lawyer denounced her son on state television for fleeing the country. A Hong Kong bookstore manager who was detained for selling books about the private lives of Chinese leaders said after his release that he had to make a dozen recorded confessions before his captors were satisfied.

This time, the world of women’s tennis isn’t playing along and has suggested it will stop holding events in China until it is sure Ms. Peng is truly free of government control. The biggest names in tennis — Serena Williams, Naomi Osaka and Novak Djokovic, among many others — don’t seem to be afraid to lose access to a potential market of 1.4 billion tennis fans either. The pushback is problematic because the Winter Olympics in Beijing are just weeks away from opening.

The country’s huge army of propagandists has failed its top leader Xi Jinping’s expectations that it take control of the global narrative about China. But it shouldn’t take all the blame: The failure is ingrained in the controlling nature of China’s authoritarian system.

“It can make Peng Shuai play any role, including putting up a show of being free,” Pin Ho, a New York-based media businessman, wrote on Twitter.

For Chinese officials in charge of crisis management, he continued, such control is routine. “But for the free world,” he said, “this is even more frightening than forced confessions.”

One of the biggest giveaways that Ms. Peng isn’t free to speak her mind is that her name remains censored on the Chinese internet.

“As long as coverages about her inside and outside China are different, she’s not speaking freely,” said Rose Luqiu, an assistant professor of journalism at the Hong Kong Baptist University.

Despite the outpouring of concern about Ms. Peng’s well-being on Twitter and other online platforms that are blocked in China, the Chinese public has little knowledge of the discussions.

Late Friday night, as the momentum of the hashtag #whereispengshuai was building on Twitter, I couldn’t find any discussion of the question on Chinese social media. Still, Ms. Peng had clearly caught the attention of politically observant Chinese. I messaged a friend in Beijing who was usually on top of hot topics and asked generally, in coded words, if she had heard about a huge campaign to find someone. “PS?” the friend guessed, using Ms. Peng’s initials.

It’s hard to estimate how many Chinese people learned about Ms. Peng’s allegation, which she detailed in a post on Chinese social media earlier this month. Her post — which named Zhang Gaoli, a former top Communist Party leader, as her assailant — was deleted within minutes. One Weibo social media user asked in a comment whether saving a screenshot of Ms. Peng’s post was incriminating. Another Weibo user, in a comment, described being too scared to share the post.

They have good reasons to be afraid. Beijing has made it easier to detain or charge people for what they say online. Many people get their social media accounts deleted for simply sharing content that the censors deemed inappropriate, including #MeToo-related content.

China has been bitter about its poor image in the Western mainstream news media and has talked for years about taking control of the narrative. Mr. Xi, the top leader, said that he hoped the country would have the capacity to shape a global narrative that’s compatible with its rising status in the world. “Tell the China story well,” he instructed. “Create a credible, lovable and respectable image of China.”

Official media has raised the suggestion that Covid-19 emerged from a lab in the United States and spread the unproven allegation on Facebook and Twitter. China released thousands of videos on YouTube and other Western platforms in which Uyghurs said they were “very free” and “very happy” while the Communist Party was carrying out repressive policies against them and other Muslim ethnic minorities in the Xinjiang region.

In reality, China is less respected, and its narratives less credible, since Mr. Xi took power nine years ago. He cracked down on relatively independent media outlets and eliminated critical online voices within the country. He unleashed diplomats and nationalistic youth who would roar back any hint of criticism or belittlement.

“There are three things that are inevitable in life: life, death and humiliating China,” a reader commented on a recent column of mine.

Despite China’s relatively fast economic growth and relatively competent response to the pandemic, the country’s deteriorating human rights records and its uncompromising international stance are not helping its image. The negative views of China in the vast majority of the world’s advanced economies reached a historic high last year, according to Pew Research Center.

China can’t respond to the questions about Ms. Peng effectively because it can’t even address the problem directly.

The subject of Ms. Peng’s sexual assault allegation, Mr. Zhang, had been one of the Communist Party’s most powerful officials before he retired. The party sees criticism of a top leader as a direct attack on the whole organization, so it won’t repeat her allegation. As a result, the state media journalists who are trying to argue that Ms. Peng is fine can’t even refer to it directly.

For Hu Xijin, the editor of the nationalist Global Times tabloid, the allegation against Mr. Zhang has become “the thing.” “I don’t believe Peng Shuai has received retaliation and repression speculated by foreign media for the thing people talked about,” he wrote on Twitter.

Mr. Zhang can’t even be discussed online in China. Those who do call him “kimchi” because his given name sounds like the name of an ancient Korean dynasty.

If Mr. Hu, China’s spin master, could speak more plainly, and if the Chinese people had the freedom to discuss Ms. Peng and her allegation, official media might understand how to build a narrative. Instead, Mr. Hu alternates between trying to change the conversation and trying to shut it down completely.

“For those who truly care about safety of Peng Shuai, her appearances of these days are enough to relieve them or eliminate most of their worries,” he wrote. “But for those aiming to attack China’s system and boycott the Beijing Winter Olympics, facts, no matter how many, don’t work for them.”