A most unusual topic. I wonder, though: is the appearance of a Nazgul "under the robes" any more real than Sauron's appearance as a flaming red eye? What Frodo "sees" when he puts on the Ring may be no more their true appearance than when he sees the Eye through the auspices of the Ring. It may be a representation of what they once were (or in Sauron's case, a frightening image he wishes to project into the minds of others to terrify them), but not real in a physical sense. When Merry stabs the Witch King, he breaks the spell that "knit his unseen sinews to his will," allowing Eowyn to finish him off, so it seems plain to me that there is some form of "magic" at work in his continued embodiment -- a living death, of sorts, and rather more akin to the faded Elves, as others have noted.
Must ponder this some more (and maybe go rooting through the letters and such...)