If I take damage to my capital in a way that allows me to choose which zone takes the damage, there is nothing in the rules that prevents me from assigning the damage to a burning zone. Yet playing this way breaks a number of cards in practice, so I've houseruled that you can't do that. Besides, it seems the intent not to be able to assign damage to a burning zone. Still, the rules do not disallow this.
Also, might this possibly be worthy of an erratum / rules clarification / place in the faq?