On the off the record briefing, the press says "White House Sources say", or the administration thinks... etc.
Basically, it is an anon briefing. If they wanted to be quoted on the record, they would have gone on the record. The concept that a person giving something off the record, can later be payed back by the White House, by giving up his anonymity, without his/her consent, is chilling to me.
Any whistleblower in any administration will stop saying anything meaningful to the press even off the record, if they know that they actually don't have any confidentiality. Their words are entirely the property of the President, to be used against them at a later time. Yes, this damages Clarke, but I think that isn't an important enough issue to go across this murky line.