For free falling, pearl necklace would be a better thought experiment than elevator. There will be other examples too. A real example is Comet Shoemaker-Levy 9, which fell on Jupiter in 1994.
Common theory of Mercury's perihelion shift is poor. Also, Newton's shell theorem should be reconsidered.
We can say that we can quantitatively grasp both gravity and inertial force. However, we cannot qualitatively grasp them. Do we have the right to preach equivalence principle ?
In fact, perhaps equivalence principle can be directly denied.