Well, I can see your point. Logically, it would seem to me that the adamantite would go through the DR, but not serve as a prerequisite for enchantment, but it is true that the rules just say 'enhancement bonus' in both places. Complicating this is the description of the adamantite weapons in the 'specific weapons' section:
Adamantine Battleaxe:
This nonmagical axe is made out of adamantine, giving it a natural +2 enhancement bonus.
(This is from the SRD - I don't have a DMG handy right now, so if the wording is different there, it could make a difference.)
Note that all of the sudden, it isn't a 'natural enhancement bonus', it is just an 'enhancement bonus'. So the question becomes: when they say 'natural enhancement bonus', is the word 'natural' part of the rules text, or a clarifying adjective. I tend to come down on the side of 'clarifying', since it does not stack with other enhancement bonuses and the rules are generally pretty consistent about allowing differently named bonuses to stack.