The Dead Sea Scrolls and the mustache?

THE AMERICAN MUSTACHE INSTITUTE reports the following:

We should note biblical text -- specifically the Dead Sea Scrolls -- which specifically state that "each time a mustache is shaved, an angel in heaven dies and falls to earth."

Relayed on the PBS website by Paul Solman, who rightly has his doubts. It's a fine apocryphal saying, but it isn't in the Dead Sea Scrolls.