On Hoppe's Derivation of the Private Property Ethic

I've had some time to mull over Hoppe's derivation of the private property ethic (available here), and though I find it extremely interesting, I think I have found major, though perhaps not insurmountable a flaw.

Hoppe's argument proceeds essentially by excluding all other ethics besides the private property ethic. As I understand it, it is essentially this:

1) Any argument that is inconsistent with the ability to argue is self contradictory
2) To argue, one must be able to use one's body and to appropriate other property by the use of it
3) Combining 1 and 2, all ethics besides the private property ethic are invalidated, so the private property ethic must be true.

The problem I see lies in 3. I don't think all other ethics are eliminated. For example, what might be called the 'anything goes' ethic is still valid. The ethical principle that anyone is justified in doing what they can do by force or otherwise still satisfies this rule, so the private property ethic is not the only valid ethic.

I am still quite happy with this meta-ethical rule however, because it demonstrates two special and important ideas. First, as Hoppe explicitly shows in his paper, the argumentation-consistency rule bars any sort of collectivism. This is important because it bars the most popular ethical opponents to the private property ethic. Second, Hoppe's argument suggests that one can indeed derive ethical principles from objective truths, even if it doesn't quite do so itself. I am optimistic that such a derivation can and will be made.

UPDATE:
I think that what Hoppe has proven is that of all what might be called 'property ethics' the private property ethic is the only self-consistent one. Property ethics are those that claim that the rightness or wrongness of an action depend on whether the actor has ownership over the subject of the action, and that ownership is non-overlapping; that is, no two actors can claim the same ownership over some subject (though they could share ownership through some agreement).