True, it's more of a metaphor. Point still stands, though!

Sauron is essentially a spirit, albeit an extraordinarily powerful one. He is able to take many different physical forms, and once had a reputation as a shapeshifter. However, when he made the One Ring he put most of his power into it, so that he could better control it and therefore the other rings of power. It isn't that his physical form isn't visible when he doesn't possess the Ring, it's more that he doesn't have the power to manifest it in the same way. All he's capable of is the form of the Eye, and that's only after centuries of regathering his strength.