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)