I'll keep the requester of this one anonymous, for reasons that will become obvious (it's not anyone I work with, so rest easy, Courier-Journalists). The requester was looking for a word to describe someone as clueless without the clueless one realizing it.
My standard toolbox for Pimp My Word, Webster's New World Roget's A-Z Thesaurus, didn't have an entry for clueless. So I checked ignorant, but most of the words there were too obvious. Ignorant led me to stupid, which had some good ones (cracked, addleheaded and damn-fool among them), but still nothing that might leave the target "groping in the dark" (another suggestion from stupid). But stupid suggested the second entry for shallow, and there I struck gold: piffling.
The American Heritage Dictionary explains what it means to piffle: "To talk or act feebly or futilely." The OED's definition is even more fun: "To talk or behave in an ineffectual way; to talk nonsense, to witter; to dither or fiddle."
Sounds pretty clueless to me, and obscure enough that it could just slip past an empty head.
The dictionaries say piffle's origin is unknown, though Merriam-Webster Online suggests: "perhaps blend of piddle and trifle." M-W and the OED date it to the mid-19th century.