But I understood him as disagreeing, not just with Barbour, but with a whole lot of physicists (including me) who are "B-theorists" which is a horrible term that means you consider the whole history of the universe as the fundamental reality and see change as a thing observed by beings within it.
But that doesn't mean I think physics, or the history of the universe are time symmetric. My own view is there is some fundamental (but not very well understood) time asymmetry in physics. Yet I am still a B-theorist.
But the alternative called "A-theory" (which I think Maudlin believes) is that time, and change are more fundamental than physics, so the fundamental reality is "the state of the universe _now_" and the laws of physics tell us how it has changed and will change.
A-theory is also perfectly cogent, but it is separate from time symmetry. The only link being: IF physics is time symmetric (which it isn't) THEN B-theory implies there is no fundamental difference between time directions, while A-theory still allows it.