The Equivalence Principle tells us that Spacetime has a geodesic (projective) structure with a non-integrable connection. It has been argued that the Equivalence Principle distinguishes the metric theories of gravitation from non-metric theories. So, one can get the deflection of starlight from other metric theories.
For instance, in E. Cartan's spacetime formulation of Newtonian Gravity, the spatial hypersurfaces were flat, although the full spacetime structure was curved. I haven't checked this for myself, but it seems that if you pretend that a photon has some kind of mass associated to it, you can get a deflection of starlight. However, you might get only half of the measured value.
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