I find myself disagreeing still. I would say that the idea that you can't measure your own motion without something else to measure against, is obvious to the casual person. (Whether that "something" is a physical object, the background radiation, the luminiferous aether, or whatever.) The possibility that it might not be true is actually far less intuitive, since it would require there to be some intrinstic frame of reference that is impossible to leave behind, even in a thought experiment.
I think using the word "obvious" is very misplaced here. Obvious would suggest that fully understanding the statement is something the casual person would arrive at given no help or extraneous thought into the statement. This is simply not true given what we know about the average intelligence of humans.
So you're saying that what laymen mean when they intuitively understand that you can't measure your own motion is something else than what is meant by a physicist in the context of relativity. In particular a physicist means that you can't do that even when you have access to light, or those other things. A layman understands that you can't measure whether you're moving without access to those things, but he does not understand that it's still impossible with access to those things. In that case you cannot appeal to layman intuition on the former to conclude the latter, which is exactly what's necessary for an understanding of relativity.
Also, even with this interpretation it's questionable. In Aristotle's mind you can determine whether you're moving or not, even if you are completely alone in the universe. You take an object that you have with you (e.g. your t-shirt), throw it in a random direction with a specified velocity relative to you. According to Aristotle both you and the watch will decelerate. But since the deceleration is relative to the absolute reference frame in which you will eventually come to a halt, you can deduce whether you're moving from the relative deceleration between you and your watch (although interestingly if the deceleration has a special form, then you cannot determine whether you are moving, but that is again a non trivial fact that is not obvious to a layman). To Aristotle, and the people after him until Galilei, the idea of a special reference frame was perfectly intuitively obvious! (though, of course, incorrect)
This whole thread of discussion seems irrelevant to me. The article is obviously not intended to provide a rigorous treatment of relativity. It is not meant to derive relativity from first principles. It is not even meant to be accessible to people who don't have prior knowledge of relativity. It is meant to be funny, and it succeeds at that.
You can measure acceleration without needing a special frame. More significantly, you can measure rotational motion without something to measure against.
See that Feynman quote I linked in my original post; he discusses exactly this point.
But the argument you used would seem to apply to both of those thing. That's what makes it flawed -- you claim it is obvious, when in fact this line of argument is very subtle and often misleads laymen. (Notice that in this very thread there seem to be people who think you couldn't detect acceleration.)
