Sounds like the Iraqi police are lying about never detaining Berg. No doubt the existence of the Israeli stamps in his passport were communicated to al-Zarqawi's followers by someone in the Iraqi police force. Why the FBI was questioning him is anybody's guess.
"Detained" is not the same as "arrested", although it may look and feel about the same. So the Mosul chief of police may have been correct in a technical sense. Nick Berg was not "arrested", but he probably spent several days in custody, primarily for his own protection.
But the password? Too improbable. Berg may have not exercised the necessary caution in protecting the password, but to say that he gave it up willingly to Zaccarias Moussaoui just strains credulity too far.
Well, since al Qaeda's offered a reward for the capture of any American soldier or contractor, it might be worth checking out Mr. Police Chief to see if he's acquired any inexplicable new wealth. And better check out those inlaws and hotel staff, too.