Sorry to disagree with you, Tartan, especially since it is such a long time since I last saw you, but a coot is a water-bird which actually has a bare - ie featherless - patch on its forehead, rather than white feathers. The Oxford English Dictionary has this to say about the bird: "having the base of the bill extended so as to form a broad white plate on the forehead (whence the epithet bald)."
So, this bare patch or plate...sometimes also called a shield...is the source of the 'bald' claim.