I'd say there's no reason to question what you've read and understood ... nor to question what you've read and fallen for.
Given the profound ignorance of ancient texts as well as ancient historical sources which Julian Jaynes displayed in The Origins of Consciousness in the Breakdown of the Bi-cameral Mind, reputable scholars of ancient texts and historical sources have as little respect for that work as do Jaynes' fellow philosophers--which is to say, not very damn much. Jaynes' thesis is interesting, even compelling--it is in no way an accurate description of ancient scripture and historical sources as they are known to those who have spent their lifetimes studying them.
Very good point, Set - characterizing of Jaynes' work as being "not beyond disput" doesn't go to the half of it. Apart from Jaynes' ignoring the development of Eastern thought, there is the matter of his assertion that literary evidence of introspection was a post-Homeric development; the concept exists unmistakably in such vastly earlier writing as The Epic of Gilgamesh, and may be argued to be present scattered throughout the earliest of the Upanishads.
Aside to gunga - I happen to have a couple copies of Breakdown at hand, both Houghton-Mifflin, an original 1976 hardcover edition, ISBN 0395207290, and a 1990 Trade Softcover edition, ISBN: 0395563526 (textually differing from the former only with the addition of a retrospective afterword by Jaynes). I just gotta ask - what edition do you have?