When House Republicans called a hearing in the middle of their long recess, you knew it would be something big, and indeed it was: They accidentally blew the CIA’s cover.

The purpose of Wednesday’s hearing of the Oversight and Government Reform Committee was to examine security lapses that led to the killing in Benghazi last month of the U.S. ambassador to Libya and three others. But in doing so, the lawmakers reminded us why “congressional intelligence” is an oxymoron.

Through their outbursts, cryptic language and boneheaded questioning of State Department officials, the committee members left little doubt that one of the two compounds at which the Americans were killed, described by the administration as a “consulate” and a nearby “annex,” was a CIA base. They did this, helpfully, in a televised public hearing.

Rep. Jason Chaffetz, R-Utah, was the first to unmask the spooks. “Point of order! Point of order!” he called out as a State Department security official, seated in front of an aerial photo of the U.S. facilities in Benghazi, described the chaotic night of the attack. “We’re getting into classified issues that deal with sources and methods that would be totally inappropriate in an open forum such as this.”

A State Department official assured him that the material was “entirely unclassified” and that the photo was from a commercial satellite. “I totally object to the use of that photo,” Chaffetz continued. He went on to say that “I was told specifically while I was in Libya I could not and should not ever talk about what you’re showing here today.”

Now that Chaffetz had alerted potential bad guys that something valuable was in the photo, the chairman, Darrell Issa, R-Calif., attempted to lock the barn door through which the horse had just bolted:

“I would direct that that chart be taken down,” he said, although it already had been on C-SPAN. “In this hearing room, we’re not going to point out details of what may still in fact be a facility of the United States government or more facilities.”

May still be a facility? The plot thickened — and Chaffetz gave more hints. “I believe that the markings on that map were terribly inappropriate,” he said, adding that “the activities there could cost lives.”

In their questioning and in the public testimony they invited, the lawmakers managed to disclose, without ever mentioning Langley directly, that there was a seven-member “rapid response force” in the compound the State Department was calling an annex. One of the State Department security officials was forced to acknowledge that “not necessarily all of the security people” at the Benghazi compounds “fell under my direct operational control.”

And whose control might they have fallen under? Well, presumably it’s the “other government agency” or “other government entity” the lawmakers and witnesses referred to; Issa informed the public that this agency was not the FBI.

“Other government agency,” or “OGA,” is a common euphemism in Washington for the CIA. This “other government agency,” the lawmakers’ questioning further revealed, was in possession of a video of the attack but wasn’t releasing it because it was undergoing “an investigative process.”

Or maybe they were referring to the Department of Agriculture.

That the Benghazi compound had included a large CIA presence had been reported but not confirmed. The New York Times, for example, had reported that among those evacuated were “about a dozen CIA operatives and contractors.” The paper, like The Washington Post, withheld locations and details of the facilities at the administration’s request.

But on Wednesday, the withholding was on hold.

The Republican lawmakers alternated between scolding the State Department officials for hiding behind classified material and blaming them for disclosing information. But the lawmakers created the situation by ordering a public hearing on a matter that belonged behind closed doors.

Republicans were aiming to embarrass the Obama administration over State Department security lapses. But they inadvertently caused a different picture to emerge than the one that has been publicly known: that the victims may have been let down not by the State Department but by the CIA. If the CIA was playing such a major role in these events, which was the unmistakable impression left by Wednesday’s hearing, having a televised hearing was absurd.

The chairman, attempting to close his can of worms, finally suggested that “the entire committee have a classified briefing as to any and all other assets that were not drawn upon but could have been drawn upon” in Benghazi.

Good idea. Too bad he didn’t think of that before putting the CIA on C-SPAN.