Really, what was this all
about?
As far as I can work out, the reasoning is that since Legolas was the first to yell when the Balrog appeared, he must have been the only one to know what a Balrog was, therefore he must have seen one before, therefore he must be a First Age Elf, therefore he must be Legolas of Gondolin!
Makes the Arkenstone/Silmaril case look positively watertight!
