According to CorkMasters, cork forests are indeed nearly natural: the cork is harvested off trees without permanently harming the trees, and no herbicides, fertilisers or irrigation are needed. Although a cork forest must involve some meddling with nature (keeping access roads to trees clear, perhaps even mowing around trees, perhaps removing other kinds of trees), it seems the WWF have no problems with this kind of agricultural impact.
This relates to Dan Simon's elucidation of the idea of inaction as it applies to the precautionary principle. Is "inaction" continuing to use cork forests as they've been used for centuries? Or is "inaction" completely stopping the "exploitation" of these forests? Ask the question again about fossil fuel use, and it's clear that most quick answers to these questions depend on ill-examined notions of what is natural and what is action, and probably a lot of indoctrination about environmental good and bad.