President Donald Trump has quickly shut the door on increased gun control in response to the mass shooting at a Texas church on Sunday. And on Tuesday he made a highly specific — and highly dubious — claim that will turn heads.

During a news conference in Seoul, Trump was asked whether he might want to also apply the kind of “extreme vetting” that he advocates for immigration to the purchasing of guns. Turns out he does not. And he actually contends that stronger gun control might have multiplied the death toll in Sutherland Springs.

Here’s how he responded:

“If you did what you’re suggesting, there would have been no difference three days ago, and you might not have had that very brave person who happened to have a gun or a rifle in his truck go out and shoot him, and hit him and neutralize him. And I can only say this: If he didn’t have a gun, instead of having 26 dead, you would have had hundreds more dead. So that’s the way I feel about it. Not going to help.”

This claim echoes what the National Rifle Association often says about such tragedies: The only way to stop a bad guy with a gun is a good guy with a gun. And many Americans agree with that. The circumstances in Sutherland Springs, where the shooter was chased away by armed civilians, would certainly seem to bolster the claim that guns can also ward off tragedy or reduce its scope.

But with this claim, Trump takes a plausible premise and stretches it beyond recognition, as he so often does. The president’s penchant for hyperbole and ignoring inconvenient facts are present here.

First, Trump’s claim that hundreds more would have died if those two civilians who warded him off didn’t have guns is highly suspect. The largest mass shooting in U.S. history — which took place in Las Vegas last month — left 58 dead. Trump is essentially arguing that the Texas shooting would have been at least eight times more deadly and four times worse than Las Vegas, which is very speculative at best and implausible at worst. And the fact that a U.S. president is so openly speculative about the scope of such tragedy is remarkable. Trump isn’t suggesting this could have happened; he’s saying it would have.

Secondly, Trump seems to be getting ahead of the facts on the ground. Trump cites “that very brave person” who was able to “hit [Devin Patrick Kelley] and neutralize him.” Kelley died, but it is not known whether he was killed by exchanging fire with the civilians or self-inflicted wounds, according to the Texas Department of Public Safety. Kelley was shot in the leg and torso before being shot in the head.

And lastly, there is no real reason to believe the increased background checks would have prevented the armed civilians, Johnnie Langendorff and Stephen Willeford, from obtaining their own firearms that they used to engage Kelley. Background checks, after all, don’t mean no one gets guns; they just mean it’s perhaps a little more difficult to get guns — that there is more of a process involved.

What we do know is that the alleged gunman was not supposed to have guns, and that the Air Force failed to follow the correct procedures to prevent him from obtaining them. As The Post’s Alex Horton reports, “Firearms retailer Academy Sports . . . confirmed Monday that Kelley purchased two weapons from its stores after passing federal background checks this year and last.” It’s not clear whether those were the weapons used.

So you can perhaps make an argument that the background checks that were already in place failed, and it’s more a matter of enforcing existing laws rather than adding new ones. But Trump takes it much further than that, suggesting such background checks might have prevented the two men from obtaining their guns in the first place, resulting in an increased death toll at the Texas church.

But he won’t concede that shored-up background checks might have impeded the gunman, for reasons that aren’t clear.

Reasonable people can disagree, but Trump is making an unreasonable argument here.

Aaron Blake is a columnist for The Washington Post.