The block quote from the book states, "Toward the end of my interview with him, [Murray] Campbell somewhat mischievously referred to an incident that had occurred toward the end of the first game in their 1997 match with Kasparov."

This suggests rather strongly that the author of the book interviewed Campbell, rather than relying on some secondary source. Campbell, of course, may be speculating, but this seems like pretty direct attribution. The only more direct source would be Kasparov himself.