He emails me an on-the-record quote:

All of our sources understood that they were being interviewed for our book. We conducted none of our interviews off the record. And we violated no agreements we made with any of our sources.

So logically, either Reid told Heilemann and Halperin these things on the record, or he didn't tell them these things in person, but told them to someone else who is the real source for the quote. I have asked John to clarify this. Stay tuned.

Update from JH:

As we wrote in the authors' note, all our interviews were on deep background. But we haven't confirmed that we talked to reid or anyone else -- because we promised all our sources that we would not identify them.

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