What burden? The burden is on the owner, because he has all his assets being seized, making it much harder to defend himself now. That should never happen - certainly not in a "innocent until proven guilty" system (if that's still the case).
I think rhino369's point is that, whatever procedural arrangement might characterize the discourse, the actual burden of proof is on the owner - if they take action and prove their case, they get their possessions back. Until that time, the possessions are in the custody of the state.
Furthermore, I don't think it's true (at least not per the article) that a civil forfeiture proceeding puts a burden of proof on the state - it seems to be that the owner has an opportunity to petition for appeal, which if not taken, amounts to a forfeit by default.