Payne's pivotal claim: verse 15 shows hair done up IS the covering (not analogy)

Payne reads verse 15 ('her hair is given to her for a covering') as the key to the whole passage: every reference to 'covering' earlier meant hair done up. This is NOT an analogy (as the traditional view holds) but a direct identification. Long hair alone is not the covering -- it must be done up. This creates a problem: the verse says 'if a woman has long hair, it is a glory to her, for her hair is given to her for a covering,' which on face value makes long hair (not done-up hair) the covering.