I think he meant a theory, not theories. Kind of like how fundamental F=ma is to motion, or Conservation of Energy, or Conservation of Matter. Having lots of different halfway working theories is a sign of a science still being developed as far as theory goes. Not that I think I will see such a thing for the brain in my lifetime, but I'm not discouraged from working towards it yet.
I believe Physics is topdown. Physics, for example started off with very intuitive guesses and generalized concepts based on direct experience (aristotle). As it became more grounded in reality and experimental verification became important, it became a little bit less intuitive, but not terribly unintuitive (classical physics, starting with Kepler and Galileo and ending). Newton tied the general basic theory together rather nicely with his three laws.
(I have no idea where conservation comes from historically... it kind of sneaked in to the classroom.)
And the quantum mechanics came along and described, more fundamentally, the classical observations with crazy unintuitive ideas.
But "top-down" and "bottom-up" describe linear models of discovery. It may be that this is how the community of scientists develop science as a whole, but it doesn't mean that particular scientists are restricted to viewing things that way.
Now that I think of it, we almost nearly always have to test thing from the bottom-up, because once we learned quantum mechanics, for instance, there were theories in classical physics that became invalid as they had made fundamental assumptions that were not true in general. But as far as I know, you can recover nearly all of classical with quantum when you make those same assumptions with QM and take the limit. So we see a sort of way we can quantify reductionism.
I've gone off on a tangent, but what I'm trying to say is that we should generally always be able to recover the top from the bottom if we make the right assumptions at the bottom. And the top will always make sufficient predictions in the limit that we're generally comfortable with because it generalizes the intricate parts of the bottom, so both schools of thought "bottom-up" and "top-down" are valid in a sound scientific theory.
Anyway, in some sense, I predict that neurology will be the QM of psychology (which will play the part of classical physics).