Might be on micro film....or been copied to a CD.
If you read the article carefully, it seems the Archives staff caught Berger red-handed (he "misplaced" a document they gave him), and so they then gave him "marked" copies (read "traceable") which he promptly stuck in his pants, coat and briefcase before he waddled out...
Sounds like he was either 1) desperate; or 2) confident that he wouldn't face any real consequences. If recent history is any guide (lost e-mails, Whitewater and FBI files, classified CIA docs on the director's home computer, etc., ad nauseum), I'd say it was a safe gamble.