In another sense, the GTR is in direct opposition to Mach's principle.  In Mach's universe, you cannot have a complete description of a body if you do not know the dynamics of everything else in the universe.  In contrast, the GTR is a gauge theory which deals with a strictly local field.  Fundamentally, it is hopeless to do physics with Mach's principle.  The GTR saves the science of physics because you can give a complete description from local observations.  In that sense the principle of relativity is a theory ABOUT physics rather than a theory OF physics.