It's trivially easy to set up a USA corporation that is: managed by a laywer, that is is owned by a trust in the Caymans, or a similar secrecy jurisdiction, where the beneficiaries of that trust, a.k.a. the owners, are unknown - protected by client-attorney privilege. For an added layer of security, this trust's beneficiaries could be another trust that is governed by bearer bonds. That is, whoever owns the bond, an actual piece of paper, is entitled to the benefits of that trust. They are only legal in some countries.
Make this harder to follow, and you have a series of shell companies in many countries, all with secrecy jurisdictions, and I've just described how organized crime can own lots of very legal and real looking USA companies, with almost 100% chance that you'll never find out who is controlling them. Ones that make large political donations to lobby groups and politicians - not bribes you understand.
EDIT: I think you're all missing the point that this can be done today with the right lawyers and enough USD, but bitcoin just makes it easier. Though the fact that bitcoins can be traced MUCH easier than the flow of USD, is somewhat of a downside.