I looked at a 9V versus AAA batteries yesterday, and it appears that if a 9V is built of six cylindrical cells (as shown in the video, and described as quadruple-A size), then the AAAA cells would be smaller in diameter than a AAA, but about the same length.
Perhaps the idea is to use the "AAAA" cells obtained this way in place of AAA, but the capacity would be so much lower that I can't see it being worthwhile except as an emergency fix if some AAA were needed and only a 9V were available.
It would be nonsensical for a 6V lantern battery to contain AA cells; logically, if built up from a common size it would be four D cells, but taller cells of about the same diameter as a D (as shown in the link from the Snopes page) make much more sense. There are adapters available which hold four D cells and fit in where a 6V lantern battery is needed.
Good Snopes link, asianflava.
