Sometimes, the three hardest words to say in the English language are: “I don’t know.” For the U.S. intelligence community, those words could be very useful when it comes to Edward Snowden, the NSA-contractor-turned-leaker. Because when it comes to Snowden, the spooks know precious little—despite the over-sized claims made in Congress, allegedly on the spies’ behalf.

Last month, the Defense Intelligence Agency (DIA) completed a classified assessment of the damage caused by Snowden’s breach and began briefing the findings to Congress. The report is now driving a new round of claims by senior U.S. officials and members of Congress about what has been called the worst leak in U.S. history.

Director of National Intelligence James Clapper said a week ago that Snowden’s activities have placed the lives of intelligence officers and assets at risk. Sen. Susan Collins, a Republican from Maine, said if one were to stack the documents stolen by Snowden it would be three miles high. On Wednesday, Rep. Mac Thornberry, the Texas Republican who is next in line to be the chairman of the House Armed Services Committee, said the damage done by Snowden “will certainly cost billions to repair.”

But the DIA assessment is based on two important assumptions. First, it assumes that Snowden’s master file includes data from every network he ever scanned. Second, it assumes that this file is already in or will end up in the hands of America’s adversaries. If these assumptions turn out to be true, then the alarm raised in the last week will be warranted. The key word here is “if.”

What the DIA actually knows, according to U.S. officials briefed on its report, is that Snowden fabricated the digital keys—essentially assuming the identity—of multiple senior intelligence officials to gain access to classified intelligence systems well outside of the NSA like the military’s top secret Joint World-Wide Intelligence Communications System. One U.S. intelligence official briefed on the report said the DIA concluded that Snowden visited classified facilities outside the NSA station where he worked in Hawaii while he was downloading the documents he would eventually leak to journalists Glenn Greenwald and Barton Gellman. On Tuesday, Clapper himself estimated that less than 10 percent of the documents Snowden took were from the NSA. The implication was that the other 90 percent were from other spy agencies, and from the American military.

Those findings are important. But they do not necessarily mean the sky is falling. The DIA’s assessment assumed that every classified system Snowden visited was sucked dry of its data and placed in a file. DIA director Gen. Michael Flynn put it this way on Tuesday in testimony before the House Permanent Select Committee on Intelligence: “We assume that Snowden, everything that he touched, we assume that he took, stole.”

The U.S. intelligence official briefed on the report said the DIA was able to retrace the steps Snowden took inside the military’s classified systems to find every site where he rummaged around. “Snowden had a very limited amount of time before he would be detected when he did this, so we assume he zipped up the files and left,” this official said.

Bruce Schneier, a cybersecurity expert and cryptographer who Greenwald has consulted on the Snowden archive, said it was prudent to assume that lest some of Snowden’s documents could wind up in the hands of a foreign government.

The easiest way, he added, would be to go after the journalists who received Snowden’s leaks. “If anybody wants the documents, they go after Greenwald, (Laura Poitras) or Gellman.”

But he also said that this file would likely be encrypted—and that encryption today is powerful enough to be essentially unbreakable. So intelligence services may have the documents without being able to read them.

And those journalists might only have a fraction of what Snowden took. In statements and interviews, Snowden himself has been tight-lipped about any kind of master file that may exist containing everything he took from the U.S. intelligence community. In June, Greenwald told the Daily Beast that he did not know whether or not Snowden had additional documents beyond the ones he gave him. “I believe he does. He was clear he did not want to give to journalists things he did not think should be published.”

Snowden, however, has implied that he does not have control over the files he took. “No intelligence service—not even our own—has the capacity to compromise the secrets I continue to protect,” he wrote in July in a letter to former New Hampshire Republican senator Gordon Humphrey. “While it has not been reported in the media, one of my specializations was to teach our people at DIA how to keep such information from being compromised even in the highest threat counter-intelligence environments (i.e. China). You may rest easy knowing I cannot be coerced into revealing that information, even under torture.”

Some allies of Snowden have speculated that any kind of master file of Snowden documents could only be accessed through a pass code or cryptographic key broken out into pieces controlled by several people in multiple jurisdictions throughout the world. That way. No one government could force a single person to give up access to Snowden’s motherlode.

But these kinds of security measures are not comforting to others. Rep. Mike Rogers, the Republican chairman of the House Permanent Select Committee on Intelligence told two reporters Tuesday that Snowden would be foolish to think he could outsmart Russia’s intelligence agencies.

“If he really believes he has created something the Russian intelligence services can’t get through, then he is more naïve than I think he already is,” Rogers said. “That makes a huge leap of assumption that a guy by the way who has not been quite honest about how he got where he was and what he stole and for what purpose to believe the fact that no one can get to this but me. I don’t believe it.”

In an email to the Daily Beast, Gellman said he was taking many precautions to protect the Snowden archives. “I assume that I am more interesting than I used to be to foreign intelligence services,” he said. “I’m well aware of my responsibility to protect the Snowden archive. The Post and I have taken very considerable measures to secure the material physically and electronically, with the benefit of top-flight expert advice. That’s all I want to say about it.”