[dnautics]

> That is, if I fire Alice light beam at you from a moving train, while Bob fires a beam at you from a platform, both beams will reach you at the same time.

That's wrong. Simultaneity is ill-defined in relativity.

The correct example is, "if Alice fires a light beam at you from a moving train and Bob fires a light beam from you from the platform, you will measure the Alice photons as going equally fast as the Bob photons.

[tsimionescu]

Absolute simultaneity is ill-defined, but simultaneity in my frame of reference does exist.

However, you're right, your formulation is more precise, and actually possible to measure.