Subject it to experiment. You will find I am devastatingly correct.
Again. The measured quantity in a vacuum should closely approximate the derived constant. But they are not the same things. If you took your measurement inside of a diamond, it wouldn’t be very close at all. Does that change your constant? No. C is a constant. c is a measured variable. Stop confusing them.
Suppose you send to your colleague living near a black hole a measuring device exactly 1 meter long, and an atomic clock. Your colleague uses these generous gifts to measure the local speed of a photon, and your colleague measures 300,000,000 m/s. Why is this not possible? I’m still not convinced by “because we define it that way”.
But hang on a second, the length of the ruler depends on the electromagnetic repulsion between the atoms in the ruler, which depends on the local value of c, also the period of the atomic clock depends on the electromagnetic properties of the atom, which also depend on c. This will “distort” the measured value of the speed of a photon to 299,792,458 m/s or in other words no variation in the measured value of the speed of the photon will be observed and so we take c to be 299,792,458 m/s rather than 300,000,000 m/s.
How do you know the metre stick will stay the same length? If c has changed the speed of the interchange of forces between the components of the stick will have changed. Indeed a whole gamut of derived things will change. Even the size of atoms will change. Which means your atomic clock will not behave the same. Alternatively, nothing changes at all, because causality has the same metric in both time and space, and the entire thing cancels out. ETA - Ninja’ed 
The entire nature of physical reality is governed by the notion of causality. c is the speed that causality moves at in 4D space. It isn’t just the speed it moves in 3D space - which is what you will measure with a stick and a clock. Because it includes the time dimension as well you have to allow that not only do you measure your light beam progressing at c, but you measure your clock progressing at c as well.
I was going to suggest that you imagine communicating with an entity located there, and you describe how to measure c, without any other common knowledge. How do you do this, and how do you interpret the answer?
We don’t define it that way. It isn’t a choice of metrics. It is an intrinsic element of spacetime. Don’t get hung up the value 1. We don’t choose 1 because we like it. This isn’t the same 1 as you get when counting apples. It is the multiplicative identity. We get there by saying this:
Spacetime has 4 dimensions.
We move in spacetime at a constant, no matter what direction.
We can transform our travel in those 4 dimensions with a simple rotation. That is the nature of special relativity. Everything from standing still in space to photons zipping around works this way - and everything in between.
Thus we measure each of those dimensions using the same metric. It makes no sense otherwise.
At this point you can’t do anything but realise that c is both unitless, and unity.
You move in time at one second per second.
c = 1s/1s = 1
You can rotate that movement in 4D space to get movement in time and space, or indeed rotate it 90 degrees, so you only have movement in space, and not time. Its length stays the same. Which is 1.
You can create conversions that make the time or spatial dimensions look different, but they have the amusing property that their units actually cancel out if you look hard.
Just to take a point from what Francis Vaughan has said, because it illustrates a key idea:
That objects move through spacetime at ‘c’ is a nice little analogy that, if not thought up by Brian Greene, was certainly popularized by him, but recognizing where the analogy comes from and its limits brings us back to why c should be thought of as a constant and why it is natural to assign it a value of 1.
Objects (or test particles) are represented in spacetime not by moving points, but by curves called wordlines, that trace the past, present and future of the object. Now any take two point on that curve which represent two event in the history of the object. The average"speed through spacetime" (if we wished to define it) of the object between those two events would just be the “spacetime distance” it has travelled along the curve between those objects divided by the time it has experienced, or in other words:
“speed through spacetime” = [“spacetime distance travelled”]/[time experienced]
But by definition the time experienced by an object is the “spacetime distance travelled” in units of time! Or in other words the “speed through spacetime” is always a constant 1 if the “distance in spacetime” is measured in units of time. If we were to play around with units and measure “spacetime distance travelled” in units of distance we know the conversion factor from time to distance is just c, so the value is just c in whatever units of distance and time we have chosen. The only way to get c to vary is to use definitions of distance and time that vary with location in spacetime.
So the analogy is based on something very trivial about the nature of spacetime, but it is equally trivial that c is a constant with a value of 1 in natural units.
Typo. That’s worldlines.
Wordlines are the articles I write that trace the past, present and future of an object.
So with ‘it’s impossible to tell’, and ‘it wouldn’t make any difference anyway’, my idea dies, and I humbly crawl back into my box, never to question orthodoxy again. BTW some of you who’ve commented on this thread have been extraordinarily patient, extremely well-learned, and able to explain things in an easy-to-understand way. My most sincere thank you.