He first mentioned four countries that helped — including Russia — and then added as almost an addendum, “I also want to thank the Syrian Kurds for certain support they were able to give us.”

Later in his address, when asked generally what role the Kurds had played, Trump said only that “they gave us some information that turned out to be helpful” but emphasized that they played “not a military role at all.”

And finally, when he was asked whether the United States had relied upon “foreign intel,” he suggested it had not. “So, we had our own intel,” he said. “We got very little help. We didn’t need very much help.”

Both the tone and substance of Trump’s comments about the Kurds are in question now. The Kurds have suggested they played a much bigger role than Trump indicated, and U.S. officials have acknowledged the instrumentality of the information provided by the Kurdish-led Syrian Defense Forces.

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The SDF’s effort to join in the credit began even before Trump’s news conference Sunday, when the SDF commander, Gen. Mazloum Kobane Abdi, described the Baghdadi raid as the fruit of a months-long “joint intel cooperation.” It was understood at the time that the Kurds had provided at least some intelligence that had allowed for locating Baghdadi in northwest Syria.

Just how vital that information was, we didn’t know. But in postmortems of the raid, both The Washington Post and the New York Times describe the information as being vital. Both reported that an ISIS militant became an informant for the Kurds.

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The disaffected ISIS member had become an informant for Kurdish forces working with the Americans, the official said. And he provided critical information on Baghdadi’s whereabouts. The informant emerged in early summer, and over time U.S. officials became more confident in his credibility and reliability, the official said. Within the past couple of weeks, it became clear that, when put together with other information, the tip about Baghdadi’s location was solid, the official said. “It was a montage of a lot of pieces of intelligence that came together with a specific asset that was helpful,” the official said.

The Times also reported that the information was central to the effort but that it was hardly the only piece of information from the Kurds — even after Trump’s withdrawal from northern Syria that left the Kurds so vulnerable:

Armed with that initial tip, the C.I.A. worked closely with Iraqi and Kurdish intelligence officials in Iraq and Syria to identify more precisely Mr. al-Baghdadi’s whereabouts and to put spies in place to monitor his periodic movements. American officials said the Kurds continued to provide information to the C.I.A. on Mr. al-Baghdadi’s location even after Mr. Trump’s decision to withdraw the American troops left the Syrian Kurds to confront a Turkish offensive alone. The Syrian and Iraqi Kurds, one official said, provided more intelligence for the raid than any single country.

“More intelligence for the raid than any single country” sure seems like a far cry from Trump’s claim that “we had our own intel” and that “we got very little help.”

Trump’s version was further contradicted Monday by an interview Mazloum gave to Fox News’s Benjamin Hall. In the interview, Mazloum said the SDF provided Baghdadi’s location, details of his compound, where the tunnels were and how many people were there.

Mazloum also told NBC that the informant provided critical logistical details and other evidence, including Baghdadi’s dirty underwear and a sample of blood for use in DNA analysis.

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Mazloum and the Kurds certainly have motivation to play up their assistance as much as possible right now, given that the United States is at a crossroads when it comes to the alliance. Trump has spoken dismissively about the Kurds for weeks and suggested the United States doesn’t really have a dog in the fight in their long-running tensions with Turkey (though he has recently decided the United States would stay in Syria to defend oil fields that are important to the SDF’s financial stability).

But Trump’s version of events as almost impossible to reconcile with what we’re hearing about what the Kurds did.

At best, Trump seems to be oversensitive to the idea that he has abandoned the Kurds and that his withdrawal was a bad idea. Perhaps he’s downplaying the role the Kurds played here because he knows that hailing their support would only make his alleged abandonment of them look worse.

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At worst, though, he feels no real loyalty to them and that this is truly just a relationship of convenience — perhaps because he was persuaded to be skeptical of the Kurds by Turkish President Recep Tayyip Erdogan.

Either way, it seems a particularly harsh stance after the Kurds played a significant if not major role in what Trump has contended was a bigger capture than Osama bin Laden.