>It would be trivial for someone close by to match that reference frame, and then what? all the machinery of the SR is valid only on the background of the fixe

>It would be trivial for someone close by to match that reference frame, and then what? all the machinery of the SR is valid only on the background of the fixed spacetime. Once you start to massage the spacetime itself, the SR is only approximation which is good only to the extent of how good fixed spacetime model is approximation of your real spacetime.