Einstein's equation of gravity can only be saved from erroneous results under strict conditions, where its product will agree with the predictions from the real geometric theory - the Bianchi identities using the exterior derivative and applied to the metric in a covariant and artifact-free coordinate system.
These strict conditions include a coordinate system free of artifacts, the zeroing of the cosmological constant, and the inclusion of a modernized gravitational potential on the right-hand side of the equation. Otherwise, Einstein's equation does not successfully capture and implement the principles of general relativity that he does clearly state.
The relativity of motion, the equivalence of accelerated frames and the experience of gravity, the equivalence of inertial and gravitational mass, and general covariance - the independence of physically real things from any coordinate system, all of these principles lead to reliable understanding.
But Einstein's equation is merely a correspondence principle, or a translation between two mathematical systems, spacetime on the left and mechanics on the right. And it contains a coordinate dependent object, the metric, so that an artifact-free coordinate system is required to avoid uncontrolled artifacts in the calculations that follow.
So the necessity of these restrictions on Einstein's equation of gravity has been adequately justified, I think.