Another possibility is that Berger knew that the Bush people had never seen this memo, so he need to look at all the drafts of it again to recall what was in it that he may have failed to brief Bush's NSC staff about. Surely he knew that Bush, Cheney, Rice, and Ashcroft were going to tell the 9/11 Commission exactly what he had briefed them on. He needed to make sure he had the right recollection of what kinds of options the Clinton administration considered but never told the Bush people about, so he and Clinton would not trip themselves up in their own testimony.
Either of these scenarios would make it important enough for Berger to risk apprehension and prosecution by taking the documents and making notes of them. It doesn't have to have been a suicide mission for the Clintons, just his own ass-covering.
The way Clinton jumped on news cameras from the get go, makes it another Clinton cover-up.
But .. Ashcroft had seen it and talked about it in his testimony before the 9/11 commission.