There are a number of passages in the Suttas that are addressed to people with particular backgrounds, and knowing something of their views makes some aspects a little clearer. This not something unique to Gombrich. Many commentators point out, for example, that the "Fire Sermon" is addressed to fire worshipping ascetics with whom the similes (perhaps metaphors in that one, but never mind...) would particularly resonate. But what Gombrich brings to the table is detailed research on beliefs such a fire worship, rather than guesses or assumptions about it.
One of the things Gombrich points out is that the traditional commentaries seriously miss the brahmanical contexts in which some of the Buddha's teachings are given. Once that is seen, it opens up the teachings even further, giving us a richer understanding of what the Buddha was saying.
Indeed. Some of the Buddha's discourses do seem to involve rejections of the errors found in brahminical teachings (as well as the doctrines of the six wandering heterodox teachers, whom he critiques by name). Since the Upanishads teach a form of eternalism and the Buddha rejected eternalism as an obstacle to liberation, the Buddha necessarily rejected the Upanishadic teachings of his day. A perfect example of this is in the latter part of MN 22.15: "And this standpoint for views, namely, 'That which is the self is the world; after death I shall be permanent, everlasting, eternal, not subject to change... this too he regards thus: 'This is mine, this I am, this is myself." If you are familiar with the teaching Atman=Brahman, you know exactly the error that the Buddha is addressing here. Otherwise, you might miss the point. (Even Bhikkhu Bodhi sets aside the Commentary to observe, "This view seems to reflect the philosophy of the Upanishads...") This sort of Atman teaching is the error I think that PeterB may be alluding to above, when he writes, "The irony is that a few hundred years later certain aspects of that which he refuted reappeared in a different form..but thats by the by in this context."
To anticipate a possible criticism from Jack, I do not mean to suggest by the above that the Buddha could not have rediscovered an eternally valid teaching that previous buddhas had discovered, merely that this rediscovery does not preclude criticizing the errors of his day, since these errors can be specific instances of more general errors addressed by the teaching.
EDIT: I corrected "eternal teaching," replacing it with "eternally valid teaching."