Did you hear the one about Barack Obama not caring about our troops? About being so obsessed with his image that he snubbed a group of injured American heroes when he learned that there wouldn’t be cameras around to capture his act of patriotic empathy?

Yeah, so did we. The story started last week, when Obama cancelled a planned trip to visit injured American soldiers convalescing at Landstuhl, an Army medical center in Germany. It gained steam when John McCain’s campaign released an ad—to be aired in Swing State Set Colorado and Pennsylvania and, via the Web, everywhere—that frames Obama as caring more about his own image than he does about the welfare of our military.

“He made time to go to the gym, but cancelled a visit with wounded troops,” the ad’s announcer intones, as, ironically, that now-famous footage of Obama shooting-hoops-with-the-troops flashes onscreen.

“Seems the Pentagon wouldn’t allow him to bring cameras,” the announcer continues.

And then, the kicker: “John McCain is always there for our troops.”

The ad’s content has been a matter of controversy since it first aired. Particularly that middle phrase: the McCain campaign’s “strong implication,” to paraphrase today’s New York Times, that Obama cancelled the troop visit once he learned it couldn’t involve cameras—once he learned, in other words, that it wouldn’t be a photo op.

But as TPM’s Greg Sargent points out, that claim isn’t true. Yes, Obama cancelled his visit, but that had nothing to do with the Pentagon’s refusal to let him “bring cameras.” The Obama campaign had never planned for the media to accompany him there in the first place; the visit was cancelled when the DOD reminded Obama of its 2006 directive against campaigning on military premises. Since the campaign had planned that Obama would make the Landstuhl visit with retired Air Force General Scott Gration, one of his military advisers, the visit could therefore be construed as a campaign stop—rather than an official visit between a senator and soldiers. “Sen. Obama did not want to have a trip to see our wounded warriors perceived as a campaign event when his visit was to show his appreciation for our troops and decided instead not to go,” Gration said in a statement Thursday night. As Sargent puts it, “This was a screw-up, but it certainly doesn’t prove inconsistency.”

We’ve known all that for a while—or the blogs have, anyway. Sargent verified the specifics of the Pentagon’s statement to the Obama campaign on early Friday afternoon. On Saturday, ABC News’s Jake Tapper noted on Political Punch that “the McCain campaign provides no evidence for the assertion that being told he couldn’t bring media had anything to do with the trip’s cancellation.” And Time’s Karen Tumulty, on the magazine’s Swampland blog, follows that up with her own declaration that “there is absolutely no evidence” for McCain’s assertion. “The campaign insists that the plan had been to leave us at the airport,” Tumulty notes, “and the military has confirmed that arrangements were being made to hold media and staff there at a passenger terminal.”

The point being: the inaccuracy of McCain’s no-cameras-no-go claim about the Landstuhl cancellation is, at this point, well documented.

Which makes it surprising—baffling, really—that the MSM coverage of the ongoing tussle tends to gloss over that inaccuracy. Reports about SnubOurHeroes-Gate have generally failed to note that the facts, in this case, work against McCain’s assessment. They frame l’affaire Landstuhl as yet another he said/he said, yet another bit of verbal sparring whose winner cannot be determined. (Hey, we’re just the press; who are we to say who’s accurate?)

Take The New York Times’s coverage of the tussle:

Over the last two days, [McCain’s] campaign has strongly implied that Mr. Obama declined to meet with wounded American troops at Landstuhl Regional Medical Center in Germany after he learned that he could not bring television cameras along.

“I know of no Pentagon regulation that would have prevented him from going there, without the media and the press and all of the associated people,” Mr. McCain said in the ABC interview.

Mr. Obama, who visited wounded troops in Iraq without notifying the news media, and has visited injured soldiers in the United States, said he was not traveling with an official delegation and did not want to politicize the visit.

Megan Garber is an assistant editor at the Nieman Journalism Lab at Harvard University. She was formerly a CJR staff writer.