No,no, no
You have lean by the thought experiment, that both theories asserts and accept that the speed is always the "same" but not comparable the same..
Remember the ruler is variants, and stretching proportional with time
As you should be able to understand, - light moves the same distance, but the measured time it takes is different for A and B..
‘A’ live in the basement of a skyscraper, ‘B’ at the top of the same building.
Both have measured the time it took a photon to travel 13 billion. from the very first star and to us..
But A’s clock (deeper in the gravitational field) is as we know ticking slower than B’s clock.
B would argue that it took the photon one minute longer to reach us – than the time A has measured. Simply because B’s clock is ticking faster than the A’s watch. The difference is probably in reality less, but it means nothing , its the same point.
We accept that the speed “c” is the same for both A and B.
When both A and B know the time and speed, A and B can only conclude that either the distance to the star that emitted photon is significantly different, which is utopian, because the universe is not likely to change shape depending on the observer who observes a process .
Otherwise, the conclusion can only be that A’s ruler (in the basement) must have changed (been longer) proportional to the time also been stretching, as a result of A’s watch is deeper in the gravitational field.
Only in this way A and B both can assert that ‘c’ is the same for both (even thou ‘c’ is not comparable the "same")