if this is so, then Robin Hood is Robin of the Twigs

Blimey O'Reilly. There should be a name for this style of writing, where an argument is built out of a disorderly stack of wild speculation and free association, held together only by the will to find something really old to believe in.

According to the OED (yes, he made me look), in the oldest usages of the word 'wood' (9th century CE) it variously means the stuff people make chairs with, the stuff people burn on fires and the places where trees grow. There don't seem to be any usages of 'wood', past or present, to mean 'twig'.