Einstein formulated his entire special theory of relativity on the premise that all inertial frames of reference must be indistinguishable by the behavior of local laws of physics. So this is to be interpreted as any non-accelerating frame is as good as the next, and motion cannot be determined based solely on local experiment. There is no absolute background metric, all motion is to be described relative to some arbitrarily set bench mark.
I can buy that perfectly well ... but I run into trouble with the General theory.
The general theory goes one step further and asserts that even accelerated frames must be described as relative. The General theory includes the special theory as a case where acceleration, (or gravitational field), is negligible. This one carries with it the stipulation that you can't determine whether or not you're in motion even if you can feel the force of acceleration, if gravitational fields are taken into account. This is to be interpreted as any frame regardless whether or not it's "non-accelerating", is as good as the next, so long as one can attribute the sensation of force to local gravitational fields.
Where the anomaly arises, (and I do not take credit for formulating this thought experiment), is when you realize that a gravitating body attracts all objects to a common center of mass. Since any two objects on Earth, in freefall, will converge on a single point (the center of mass) ... then from the reference point of either of the two objects, the distance between them would appear to be closing. But take the same set up to an accelerating elevator ... and the objects will surely fall to the floor as predicted by GR, but the distance between them will remain constant (neglecting any experimental flaws, or the negligible force of gravity between the two objects). This asymmetry between accelerated and gravitationally induced motion, could serve to shatter the principle of equivalence. I would be moved to ask, if the equivalence falls apart in that respect, then what other areas of GR are inconsistent, perhaps as a direct consequence of the anomaly or perhaps not. Was Einstein aware of this back in his time?, and did he comment on the reverberations of its inconsitancy? Did he submit a resolution?