Hungarian Prime Minister Viktor Orbán gets an impressive amount of coverage in Western media for a leader of a country of roughly 10 million. His face was emblazoned between China’s Xi Jinping and Russia’s Vladimir Putin on the “Autocracy Now” September-October issue of Foreign Affairs. He was named the New Republic’s “Oligarch of the Month” in June. He has been profiled by many prominent papers and major magazines. Orbán gets a considerable amount of attention.

That focus is likely to only become more heightened given recent geopolitical developments. During Orbán’s May visit to the White House, the prime minister gave U.S. President Donald Trump a critical analysis of Ukraine, according to media accounts. Trump “heard a sharp assessment that bolstered his hostility toward the country, according to several people informed about the situation,” as the New York Times put it. This was just 10 days before a White House meeting in which Trump instructed a series of staffers to work with his personal lawyer Rudy Giuliani on Ukraine—a meeting now at the center of the ongoing congressional impeachment investigation.

Orbán certainly had his reasons for trashing Ukraine in the White House. Hungary takes issue with Ukrainian law from 2017 that restricts the official use of minority languages, including Hungarian, by requiring that Ukrainian be the language of secondary schools. The two countries engaged in tit-for-tat diplomatic expulsions after video surfaced in September 2018 that appeared to show Ukrainian citizens in the town of Berehove receiving Hungarian passports at the Hungarian Consulate. Trump is known to be receptive to foreign leaders’ arguments against traditional U.S. foreign policy, having recently repeated, for example, Turkish talking points regarding the Syrian Kurds and Russian talking points on any number of things.

But some have interpreted the reports to mean that Orbán—and Putin, with whom the Hungarian prime minister has a close working relationship—were behind Trump’s antipathy toward Ukraine. The Vanity Fair headline on the subject read, “Report: Putin, Orbán Planted Anti-Ukraine Theories in Trump’s Head.” The New York Post went with “Putin and Hungary’s Leader Reportedly Fueled Trump’s Mistrust of Ukraine,” GQ ran its story under “Apparently, Hungary’s Autocrat Leader Got Trump Obsessed With Ukraine.” This framing, which puts the responsibility squarely on Orbán, matters. To take from recent reporting that Orbán is behind Trump’s actions, or that Trump is somehow doing Orbán’s bidding, is not only to assign insufficient agency to the U.S. president, but also to give Orbán credit that isn’t due.

Saying Orbán is influential in American politics is just not true.

Orbán is, to an extent, influential. He’s certainly influential in Hungary, where he is on his fourth (and third consecutive) term as prime minister, and where his government has, among other things, rewritten the constitution, made judges accountable to the government, made NGOs that take foreign funding register as foreign agents, and pushed out the Central European University, founded by Orbán’s former benefactor, the Hungarian-born George Soros, whom Orbán blames for many of society’s ills.* And it’s true that Orbán was speaking about illiberal democracy back in 2014, when Trump was but a glimmer in the eye of American politics. Steve Bannon, Trump’s campaign chief, has referred to the prime minister as “Trump before Trump” (though perhaps Bannon’s analysis of European politics should be considered in the context of his own political failures on that continent). In EU politics in particular, he “definitely has had influence,” said Chris Maroshegyi of global business strategy firm Albright Stonebridge Group. “It’s important that folks recognize the ramifications of continued indifference to him.” (Orbán has long stood accused of eroding the rule of law in his own country but his Fidesz party was only suspended from the European People’s Party, the EU-wide party to which it formerly belonged, this year.)

“Orbán is a pragmatic political actor as we’ve seen with his signature ‘peacock dance’ toward the EU or with his back-and-forth with the European People’s Party. He is disdainful [of] liberal democracy and wants a European order that is less rules-based so that he can get away with whatever he wants to do at home,” Zselyke Csaky, research director for Europe and Eurasia at Freedom House, explained over email.

But Americans should take care, in the wake of reports on Orbán’s White House visit, not to overstate his role in American and international politics.

For one thing, calling Orbán influential in American politics is just not true.

“It took Viktor Orbán almost three years to get an invite to the White House of the Trump administration,” Cas Mudde, a professor at the University of Georgia’s School of Public & International Affairs, noted via email. And that visit came after lobbying efforts, switching out the Hungarian ambassador to the United States “and several high-placed supporters in Congress and within Trump circles.” (The meeting also brought forth bipartisan concern from Congress, with Republican Sens. Jim Risch and Marco Rubio signing a letter that asked Trump to raise issues related to Hungary’s “downward democratic trajectory.”)

“It is highly unlikely that Trump will have changed his position on Ukraine because of Orbán,” Mudde wrote. It is more likely, he said, that Trump merely reaffirmed Trump’s own thinking on Ukraine, a country he reportedly claimed to Orbán was unfair to him in the 2016 election.

“There is a remarkable tendency within U.S. media and politics to externalize bad decisions, blaming the election of Trump on Russia and the Syria discussion on Turkish President [Recep Tayyip] Erdogan. The Orbán story fits into this,” he added.

“Saying that Orbán contributed (or contributes) to Trump’s decision-making is overblown,” wrote Melissa Hooper, foreign policy advocacy director at Human Rights First, in an email. “Media that focuses on him as a power-broker, especially in this situation with Ukraine, and says that he has real sway with the president are trying to shoehorn Hungary into the current narrative.”

Perhaps more consequentially, overstating Orbán’s influence in American politics could bolster his influence in Hungary and Europe.

If Americans assign influence in U.S. politics to Orbán and other leaders that they do not actually have, we risk “artificially increasing the importance of these authoritarian leaders, [which] they can use at home to ‘prove’ how important they are,” Mudde wrote.

Part of Orbán’s allure in Hungary, Maroshegyi said, is that “he’s making people respect Hungary again.” Just having the meeting with Trump was a victory, he said. Hungary is accused of weakening the trans-Atlantic alliance with its associations with Russia and China and its blocking of Ukraine-NATO talks.

“He’s eroding the roots of [Hungary’s] alliance with NATO and the EU, but then he’s able to say, that’s ridiculous, I’m going to the White House, we’re having these talks,” Maroshegyi said. And certainly, to not only get a meeting but then have the talks themselves talked up, he said, hurts the claims of the more “pro-Western opposition.” How could Orbán be hurting the trans-Atlantic alliance when the leader of the United States listens to him?

That, more than readers of magazines with Orbán’s face on the cover, is who loses most from the narrative of the mighty Orbán: Hungarians opposed to him. By talking up the influence of a foreign leader so as to remove the agency of our own elected leader—and, by extension, ourselves—in this situation, Americans risk actually inflating his influence, giving still more authority to a man who has already taken so much of it.