In the wake of the Orlando shootings, Donald Trump doubled down on his proposed Muslim immigration ban and not-so-subtly insinuated that President Barack Obama's interests are more aligned with the Islamic State than with the United States.Trump has a long history of skepticism about Obama's loyalties, suggesting in years past that Obama is a Muslim and that he was born in Kenya — both claims that PolitiFact found to have no basis in fact. But now Trump has a bigger and more consequential platform, speaking as the presumptive Republican nominee for president.While conspiracy theories against sitting presidents have been alleged before — some liberals alleged incorrectly that President George W. Bush orchestrated 9/11 — Trump's charges as the nominee are unprecedented, said Joseph Uscinski, professor at the University of Miami and author of American Conspiracy Theories."All presidents are accused of all sorts things, and all people running for president are accused of all sorts of things," Uscinski said. "But the way Trump has done it, he has done it more directly than any presidential candidate I have seen and any politician I have ever seen. The media doesn't know what to do."Because PolitiFact's mission is solely fact-checking, we're going to continue fact-check Trump. His commentary on the Orlando shooting included several inaccuracies that are worth exploring. His speechTrump delivered a foreign policy speech on the Monday after the shootings that repeated his call to ban Muslims from entering the country, emphasizing the dangers of immigration and "radical Islam." (The shooter claimed allegiance to ISIS, though there's no evidence yet that ISIS directed the attack.) Trump also criticized Obama and Democratic candidate Hillary Clinton for what he called weakness on terrorism.But Trump's speech included several inaccuracies that undercut the rationale behind his immigration proposals.Trump said there's "no system to vet refugees" from the Middle East. That's False. While there are concerns about information gaps, a system does exist and has existed since 1990. Refugees are subject to the highest level of security checks of any category of people traveling to the United States.The process involves multiple federal intelligence and security agencies as well as the United Nations. Refugee vetting typically takes one to two years and includes numerous rounds of security checks before a refugee ever steps onto American soil. Ultimately, according to the State Department, about half are approved, and there's no real precedent of a terrorist slipping in through the refugee system.The Orlando shooter was born in the United States, though his father is an immigrant from Afghanistan.Trump also said, "Even our own FBI director has admitted that we cannot effectively check the backgrounds of the people we are letting into America."We rated a similar claim by Sen. Ted Cruz, R-Texas, Mostly False. FBI Director James Comey has said he can't personally vet every single refugee, but he never said the government can't do it. Comey has said "there is no risk-free process" given the information gaps and challenges, particularly in conflict zones like Syria. But Comey also said there is an "effective way to touch all of our databases and resources to figure out what we know about individuals" and the system "gives us high confidence."One thing Trump got right, though, was that Clinton's position on refugees is very different than his. He said she "plans to massively increase admissions" by 500 percent.Clinton has said she would raise Obama's limit of 10,000 to 65,000 — a 550 percent increase. We rated this part of his claim Mostly True, noting that his use of the number is misleading.The State Department plans to take in 85,000 refugees from all countries in fiscal year 2016, which ends Sept. 30, and 10,000 specifically from Syria. The next fiscal year's target will be 100,000 from all countries. Admissions are also behind schedule. Halfway into the current fiscal year, the United States has admitted 2,805 Syrian refugees.Some of those refugees will likely come to Florida. Florida took in 48,816 refugees total, the majority coming from Cuba, in the fiscal year ending in September 2015. That number includes 104 people from Syria. Local resettlement agencies reported to the federal government they could take in an additional 425 refugees this year. Those refugees might or might not be Syrian, though it seems likely they would be.Trump also attacked Obama for his rhetoric, wrongly accusing Obama of going on an "apology tour.""We've tried it President Obama's way — doesn't work," Trump said, "He gave the world his apology tour, we got ISIS, and many other problems, in return."Obama's "apology tour" is a common and old Republican talking point, and it's a pretty ridiculous charge. We gave out several Pants on Fire ratings for it in the 2012 election. In 2009, Obama criticized U.S. actions like torture practices at Guantanamo, but he didn't offer apologies. Obama conspiracyTrump's attacks fall in line with his larger argument that Obama doesn't have America's best interests at heart when it comes to the Middle East. Trump continued to promote that line in media interviews in the days after the attack.For example, Trump said on "Fox and Friends" of Obama's policy on fighting terrorism, "He doesn't get it or he gets it better than anybody understands — it's one or the other, and either one is unacceptable.""We're led by a man that either is not tough, not smart, or he's got something else in mind. And the something else in mind — you know, people can't believe it," he added. "There's something going on. It's inconceivable."Trump ratcheted up the attack on Facebook a few days later, plainly saying Obama's and Clinton's foreign policy was designed to aid the Islamic State, writing, "Hillary Clinton received a classified intelligence report stating that the Obama administration was actively supporting al-Qaida in Iraq, the terrorist group that became the Islamic State."The post linked to an article by the conservative media outlet Breitbart, which contains the memo at issue. But the memo doesn't show what Trump said it did.The document outlines what is known about "the general situation" on the ground in Syria and Iraq following the rebellion against the regime of Bashar Assad. The memo notes that al-Qaida in Iraq (AQI) is one group involved in the opposition, and "the West, Gulf countries and Turkey support the opposition, while Russia, China and Iran support the regime."Experts said the memo means the United States shared a larger goal with the opposition — namely, countering Assad — not that the United States actively supported all elements of that opposition. In the byzantine world of the Syrian opposition, the United States sought to support moderate elements while opposing extremists such as AQI and, later, ISIS.That's different from the argument made by Trump — that the United States was actively supporting ISIS or its predecessors. In fact, experts say that assertion is flat wrong. The implication that the Obama administration was actively helping the United States' enemies is inaccurate. It has always been U.S. policy to oppose AQI and ISIS, and the United States has aggressively fought the group and killed its leaders for years.We rated Trump's assertion Pants on Fire.Read more at PolitiFact.com.