SilasBarta:

Yes, GR could be wrong, but for it to be wrong in a way such that e.g. you actually can distinguish acceleration from gravity would require more than just a refinement of our models; it would mean the universe up to this point was a lie.

This isn't really true. In GR, you can in principle always distinguish acceleration from gravity over finite stretches of spacetime by measuring the tidal forces. There is no distribution of mass that would produce an ideally homogeneous gravitational field free of tidal forces whose effect would perfectly mimic uniform acceleration in flat spacetime. The equivalence principle holds only across infinitesimal regions of spacetime.

See here for a good discussion of what the equivalence principle actually means, and the overview of various controversies it has provoked:
http://www.mathpages.com/home/kmath622/kmath622.htm