Quote by harrylin
Quite to the contrary: there is experimental proof that we may freely choose an inertial reference system and pretend that it is "in rest", so that the speed of light becomes (or appears) identical for both halves of the round trip measurement. Since we apply the relativity principle to light, this should be true for any inertial reference system that we freely choose.

The synchronization of clocks at A and B where tBtA=t'AtB stipulates that the clocks are both stationary with respect to each other...
How can this stipulation apply when one can't verify this prior to synchronization? Actually it would require multiple synchronization successes to verify points A and B are stationary with respect to one another wouldn't it?
... my point is that even if both A and B are inertial reference frames, that does not imply they are stationary relative to each other. They may be moving together or apart at a constant rate, or one or both may be free falling with a net acceleration between them.
If A and B are in either constant or free fall accelerating relative motion, both are inertial frames, but there are possible synchronization measures where tB1A=t'AtB will be true, yet a prior or subsequent measure will be false. So a single successful synchronization measure can give a false positive.
The reflecting mirror method stipulates stationary A and B, but what it really stipulates is that A and B happen to be a particular distance apart when the tB event occurs... and B can be moving wrt A when this happens.
The case of free falling inertial A and B may be bringing GR into this, but the case of a net constant rate distance change between A and B does not; yet the possible false positive for a successful synchronization measure still exists (meaning that the synchronization was only for a moment, the clocks were not syched before and continue to be out of synch after in spite of a momentary tBtA=t'AtB.