News on Tuesday that Twitter is appointing to its board Tesla CEO Elon Musk — who has questioned the platform’s commitment to free speech and recently bought a 9.2% stake in the company — brought hope to conservatives seeking to have former President Donald Trump allowed back on the social network.

But Twitter on Tuesday said it had no plans to bring back Trump, who was permanently banned from the San Francisco micro-blogging firm’s platform two days after his supporters stormed the U.S. Capitol on Jan. 6, 2021 in a failed bid to overturn the presidential election. Twitter in a blog post cited “the risk of further incitement of violence.”

Although Twitter’s board “plays an important advisory and feedback role,” the company said in an emailed statement, “Our policy decisions are not determined by the board or shareholders, and we have no plans to reverse any policy decisions.”

Corporate governance expert Jo-Ellen Pozner, a professor at Santa Clara University’s Leavey School of Business, said the addition of one person to a public company’s board should not make a major difference in its policies, but that Musk may be a special case at Twitter.

“The fact that he took a $2 billion-plus position in this company and got on the board right away suggests he is being paid deference and might demand deference that most people would not be able to command,” Pozner said. “I would not be surprised if there were shakeups of various sorts following this development.”

Musk in a series of tweets in March questioned Twitter’s adherence to principles of free expression. He put up a Twitter poll, saying, “Free speech is essential to a functioning democracy. Do you believe Twitter rigorously adheres to this principle?” He added, “The consequences of this poll will be important. Please vote carefully.”

More than 70% of the 2 million votes were “no,” and Musk then tweeted the question, “Is a new platform needed?”

Although Musk’s ownership stake in Twitter came to light this week, a regulatory filing shows he bought his 73.5 million shares March 14, nearly two weeks before his Twitter poll. At the time of his purchase, those shares were worth $2.4 billion. Twitter’s stock rose steeply after Musk’s stake was revealed, and the value of his shares as of Tuesday afternoon had topped more than $3.7 billion.

Conservative figures, who often use social media to complain of censorship of conservatives on social media, saw in Musk’s investment in Twitter a chance to get Trump tweeting again. U.S. Rep. Lauren Boebert (R-Colo.) on Monday said on Twitter, “Now that @ElonMusk is Twitter’s largest shareholder, it’s time to lift the political censorship. Oh… and BRING BACK TRUMP!” Trump’s former Assistant Secretary of the Treasury, Monica Crowley, tweeted Monday that Musk should “demand the end of political censorship, company-wide reform, and the reinstatement of President Trump.”

Musk himself has been accused of an inconsistent approach to free expression. In March, Tesla fired an employee after he shared videos of his experiences testing out the company’s automated-driving software on Silicon Valley roads, including a clip where his car knocked down bollards while in “full self-driving” mode, CNBC reported. In February, a former Tesla auto factory worker sued the company claiming he was fired for reporting a multitude of safety violations, shoddy oversight and racial discrimination at Tesla’s factories. In 2017, this news organization revealed that hundreds of workers fired by Tesla purportedly over poor performance were offered two weeks’ severance pay in exchange for signing legal agreements not to criticize Musk or other company executives. Meanwhile, several lawsuits, including by the state of California, have accused Musk’s company of failing to remove racist graffiti and swastikas scrawled in workplaces.

A request sent to Tesla seeking comment from Musk did not produce an immediate response.

As Tesla chief, Musk has squabbled with the Securities and Exchange Commission (SEC) over his tweeting. The agency fined him and Tesla $20 million each after he tweeted in 2018 that he had funding to take Tesla private, and in 2020 the SEC accused him of tweeting out Tesla business information without the pre-approval of a company lawyer, in violation of the settlement over the 2018 tweet.

On Tuesday, Twitter CEO Parag Agrawal, who replaced Jack Dorsey in November, used his company’s platform to announce the plan to put Musk on the board. “Through conversations with Elon in recent weeks, it became clear to us that he would bring great value to our Board,” Agrawal tweeted. “He’s both a passionate believer and intense critic of the service which is exactly what we need on @Twitter, and in the boardroom, to make us stronger in the long-term.”

Musk replied with a tweet, saying, “Looking forward to working with Parag & Twitter board to make significant improvements to Twitter in coming months!”

The Tesla CEO’s large stake should not give him extra power over Twitter management, but Musk could “have Parag Agrawal’s ear more than other directors (and) more access to top management and more influence on top management,” Santa Clara University’s Pozner said.

As for whether having Musk on board would lead to Trump coming back to the platform, Pozner believes it’s possible, but would probably involve Musk encouraging policy changes over time. Still, she said, Musk is “so unpredictable all the time it’s hard to say which way it’s going to go.”