You'll have to forgive me for being very slow on the uptake, but I'm having trouble tying this into the context of the discussion.
The distinction being drawn is between the measurement of the speed of light and the actual speed of the light.
For example, let's say that you measure the speed of light to be ca. 300,000 km/s, using your instruments; then I measure the speed of light to be ca. 300,000 km/s using my instruments, but my metre stick is contracted such that "my meter" is shorter than "your metre", and "my second" (measured by my slower clock) is longer than "your second", then it means that the actual speeds represented by those measurements are different.
In reality, the light in my reference frame took a little longer than a second to travel a distance shorter than 300,000 km/s - although our units of measurement are the same, the actual speeds represented by those measurements are different.
I do have trouble with how time is actually measured. I just can't seem to see how it is possible to measure what is supposed to be a physical property, even if it isn't considered an object.
If we take two relatively moving observers for example, where the relative velocity is something like 0.6c; there will be events in the present of one observers reference frame, that are in the past of the other (and vice versa). This suggests that the events which are in the past for one observer continue to exist.
To accept this as true, however, would require that observer to assume that, not only the past events continue to exist, but also their "past self"; the same can be said of "future" events and "future self"; each and every observer would have to make this assumption, despite the fact that this would be contrary to the empirical evidence (with regard to "past" and "future").