The glass flow myth has been dis-proven by direct experiment at least twice, and is not supported by theoretical means in any case. The source of this old chestnut is the use of "crown glass" in old windows. Briefly, crown glass was made by spinning molten glass into large disks to approximate a plate. The disk would be slightly tapered, larger at the edges due to centrifugal forces during spinning, and once cut into panes this taper has been mis-interpreted as liquid state flow of the glass.
Though I'm not a big fan of Wikipedia, the current revision of their glass article is pretty accurate.
--Hey Matt, I forgot to say nice work on the case!