Time and Tim Maudlin

Tim Maudlin seems to want to bake time into the topological structure of spacetime. E.g., see: http://fqxi.org/data/documents/conferences/2011-talks/maudlin.pdf

What I'm wondering is whether it gets him anything. More specifically - There is a theorem in "Analysis, Manifolds and Physics", Choquet-Bruhat and DeWitt-Morette, (chapter 5, page 293):

Hyperbolic structure.  A line element (direction) at x ∈ X is a 1-dimensional vector subspace of T_x (the tangent vector space at x).

Theorem: On a paracompact C¹ manifold X the existence of a continuous line element field is equivalent to the existence of a hyperbolic riemannian structure on X.

This continuous line element field essentially gives the time dimension on X.

What does Maudlin obtain that this theorem does not give him? I guess I'll have to wait to see his book due next year. There is a very readable draft introduction here.  In fact, I think almost anyone can read the introduction.

PS: there is a more recent presentation here.