USD transactions don't have to flow through the US, either nominally or in actuality. This is obviously true in the case of cash transactions which consist of

USD transactions don't have to flow through the US, either nominally or in actuality. This is obviously true in the case of cash transactions which consist of the physical transfer of small green pieces of paper in places outside the US. It is also true of bank transactions, for example the vast Eurodollar market which has been in existence since the 1950s. If a non-US bank offers USD-denominated accounts and transfers funds from one of those accounts to another, this can and does happen entirely outside US jurisdiction.