An Iraqi counterterrorism soldier stands guard near Islamic State graffiti in Fallujah, Iraq, on June 27. (Hadi Mizban/AP)

At a campaign rally outside Fort Lauderdale, Fla., on Wednesday, Republican presidential nominee Donald Trump repeatedly suggested that there were deep links between President Obama and the Islamic State militant group, also known as ISIS.

“In many respects, you know, they honor President Obama. He is the founder of ISIS," Trump said at one point.

Later, he added that his rival in November's election, whom he called "crooked Hillary Clinton," was the co-founder of the Islamic State.

This isn't the first time that Trump has implied a link between the U.S. president and the Islamic State. The businessman-turned-politician later explained his comments in an interview with CNBC, saying that he meant only that Obama's Iraq policies had helped contribute to the rise of the militant group — a common charge from many critics of Obama.

However, Trump has long been accused of using innuendo to peddle conspiracy theories. And conspiracy theories about U.S. backing of the Islamic State play into a complicated real-world situation — not just among Trump's American audience, but also in the Middle East, where the fight against the Islamic State is actually taking place.

Theories that the United States somehow backed the Islamic State have long been widespread in Iraq, with several videos online alleging to show "proof" of the relationship. “It is not in doubt,” a Shiite militia commander named Mustafa Saadi told The Washington Post last year. Saadi claims that his friend saw U.S. helicopters delivering bottled water to Islamic State positions.

This purported U.S. support was all that stood between the Islamic State and defeat, he asserted. "They are weak," Saadi said. "If only America would stop supporting them, we could defeat them in days."

At the same time, details of Obama's Muslim heritage are still fodder for rumors and debate in the Middle East. Some view Obama as a Sunni Muslim who supports the Muslim Brotherhood (and perhaps, by some extrapolation, the Islamic State), but a prominent and contradictory theory is that Obama is actually a Shiite Muslim, bent on supporting Iranian domination of the Middle East.

(In reality, Obama is a practicing Christian, and he has said that his late Muslim Kenyan father — from whom he was estranged — became an atheist later in life.)

Trump is not the first to single out Clinton, a former secretary of state, as an alleged "co-founder" of the Islamic State, either. In 2014, a number of Arabic-language social media users shared screen shots and excerpts of a Hillary Clinton "autobiography" that they called "Password 360." In one passage, Clinton appears to write that the United States, with the help of the Muslim Brotherhood, helped create the Islamic State.

The thing is, there is no "Password 360." Clinton's memoir is called "Hard Choices," and it does not contain the passage that was being shared. The hoax appears to have begun on obscure Egyptian websites before spreading to more mainstream outlets: The Lebanese Foreign Ministry even summoned the U.S. ambassador to explain the rumor, prompting the U.S. Embassy in Beirut to release a statement calling it a "pure fabrication."

There are plenty in the Middle East who play down these rumors or mock them. The response to the allegations involving Clinton and the creation of the Islamic State was telling; Arabic-speaking social media users began their own satirical Twitter hashtag to share their absurd, made-up excerpts from fake Clinton memoirs. The Middle East is fertile ground for conspiracy theories, and people are used to batting them away.

But even if not everyone believes in these theories, they muddy the water for positive U.S. involvement in the fight against the Islamic State. “What influence can we have if they think we are supporting the terrorists?” Kirk Sowell, an analyst based in neighboring Jordan who publishes the newsletter Inside Iraqi Politics, told The Post last year.

The focus on conspiracy theories in the Middle East comes from a troubling history of real conspiracies — ones in which the West was often complicit. However, the U.S. involvement in the creation of the Islamic State is both more complicated and more mundane. Many analysts would argue that the U.S.-led invasion of Iraq in 2003 was a key catalyst for events that ultimately led to the creation of the Islamic State. Despite Trump's repeated attempts to assert the opposite, records show that he did not oppose that invasion. Obama, however, did oppose it.

And while Trump told CNBC that Obama's 2011 move to withdraw U.S. troops from Iraq is why he considers the U.S. president the founder of ISIS, BuzzFeed News notes that the real estate tycoon had repeatedly called for an immediate withdrawal of troops from Iraq around that time. Moreover, Obama withdrew the troops to meet a deadline set in a 2008 agreement reached with Iraq by his predecessor, George W. Bush.

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