Again, we cannot measure the speed of light in any direction. We assign the speed of light to be c in all directions in any Inertial Reference Frame (IRF). Therefore, the time it takes for light to propagate from one spatial point to a second spatial point is only the same as it takes for the reflection to propagate back to the first point in an IRF in which the first spatial point is at rest because our definition of an IRF makes it so. In other IRFs moving along the direction between those two spatial points, the time it takes for the light to propagate along the same two paths in opposite directions are not equal.
There is no measurement, independent of previously assigning or assuming the two propagation paths to yield the same time, that will determine that they take the same time.
I don't know why this is so hard for you to accept. If you just think about Relativity of Simultaneity, you can easily see that the time it takes for light to go in two directions between two spatially separated points takes different times in different frames. Look at this post I just made for you in another thread:
https://www.physicsforums.com/showpost.php?p=4341630&postcount=30
In the first IRF diagram where the blue twin is not at rest, the time it takes for his signal to propagate to the red twin is not the same as the time it takes for the light to reflect back but in the second IRF diagram where the blue twin is at rest, the two times are equal.