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Rob Porter and Gary Cohn say Woodward's book is wrong. They just don't say how.

(CNN) The headlines are, admittedly, intriguing: Top Trump aides say Woodward book doesn't ring true!

What's that, you say? Former White House staff secretary Rob Porter and former National Economic Council director Gary Cohn are raising objections to quotes and actions attributed to them in Bob Woodward's new book, "Fear: Trump in the White House"? BIG NEWS!

Except, that's not what they're doing at all.

Axios got statements from both Porter and Cohn on the Woodward book.

First, Cohn's:

"This book does not accurately portray my experience at the White House. I am proud of my service in the Trump Administration, and I continue to support the President and his economic agenda."

Now, Porter's. (And, yes it is long, but it makes an important point):

"Having now read Bob Woodward's Fear, I am struck by the selective and often misleading portrait it paints of the President and his administration.

"As Staff Secretary, I was responsible for managing the flow of documents to and from the Oval Office and ensuring that anything the President was asked to sign had been properly vetted. The suggestion that materials were 'stolen' from the President's desk to prevent his signature misunderstands how the White House document review process works — and has worked for at least the last eight administrations.

"It was also my responsibility to help ensure that relevant viewpoints were considered, that pros and cons were evaluated, that policy proposals were thoroughly vetted, and that the President could make decisions based on full information. Fulfilling this responsibility does not make someone part of a 'resistance' or mean they are seeking to 'thwart' the President's agenda. Quite the opposite.

"President Trump invites robust discussion and asks probing questions. He has the confidence to allow advisors to disagree with a proposed course of action and advocate for an alternative outcome—and I sometimes did just that. But in the end, President Trump is the one who decides, and he has shown himself more than capable of doing so.

"During my time in the White House, I sought to serve the President's best interests and to help enable his many successes—successes that Mr. Woodward's book ignores.

"President Trump's accomplishments are undeniable: significant tax relief to spur economic growth, rolling back burdensome regulations to unleash job creators, remaking the federal judiciary to uphold the Constitution, and much more."

Now, ask yourself, what specifically is being rebutted here?

The one detail both statements call into question is Woodward's reporting that Porter and Cohn regularly took documents off the President's desk without him knowing in order to circumvent his worst instincts.

But Porter's statement doesn't actually -- if you read it carefully -- say that Woodward got this detail wrong. It says he misunderstood this detail. Porter doesn't go into any specifics about how Woodward misunderstood the removal of documents from Trump's desk, however, so even on this front, you have to take him at his word.

That's particularly problematic for Porter, given that he was removed from the White House after allegations of domestic abuse surfaced from both of his ex-wives. Porter denied the allegations but never provided any substantive evidence to prove that he was right and they were wrong.

What both Porter and Cohn are doing in these statements is trying to make good with Trump without actually saying much of anything. These statements amount to tacit acknowledgments that Woodward got it right -- but, but, but he didn't include all the nice stuff I said about the President! Which is, of course, beside the point.

The title of Woodward's book -- "Fear" -- is apt here. Porter and Cohn may well be regretting their cooperation with the famed Watergate reporter. They likely got an earful from the President or someone very close to him when CNN and The Washington Post first got their hands on the book and pulled out a few episodes dealing with Porter and Cohn. But buyer's remorse -- or, more accurately, source remorse -- isn't the same thing as raising substantive questions about specific details in the Woodward book.

Here's the thing: On one side of this equation is Bob Woodward. His record as a reporter. His coverage of the last eight presidents. His notes, transcripts and audio recordings for this book. The book itself, which runs more than 400 pages. On the other side are the likes of Porter (who has major credibility issues) and Cohn. Their specifics-free denials. Their clear motivations for trying to muddy the waters.

It's not a close competition. Given Woodward's track record of reporting and being right, it's not enough to simply say, "This doesn't sound like the White House I know." What, specifically, did Woodward get wrong? What's the "real" story? And how can Porter, Cohn, Trump or anyone else who has denied this story prove that Woodward got it wrong and they are right?"

Those are the questions you need to ask whenever you see one of these "denials" over the next few days. Anyone can say anything. Very few people can back that talk up. Unfortunately for this White House, Bob Woodward is one of those people.

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