the key principle of general relativity is the equivalance principle: there is no (local) way to tell if you're being accelerated (in a spaceship for instance) or in a gravitational field. in other terms the inertial mass is the same as the gravitational mass.

this, and lorentz invariance, yields general relativity almost uniquely, so it's a very strong principle.

so yes, in some sense gravitation shift the notion of "inertial frame of reference"