I'm not sure this is quite true. There is a thriving and legitimate market in "eurodollars", deposits denominated in US dollars but held outside the US, and specifically beyond the reach of US authorities.
The question is whether you would be able to make much use of such deposits without US cooperation. It would definitely be difficult, but it might be possible. I am by no means an expert on this, but i came across an interesting case from the '80s - Libyan Arab Foreign Bank v Bankers Trust Co. Section 3.4 of this book describes it:
https://books.google.co.uk/books/about/Freezing_Assets.html?...
And there's a wider discussion here:
http://digitalcommons.wcl.american.edu/cgi/viewcontent.cgi?a...
The upshot is that a UK judge decided that it was possible to pay out a dollar balance held in London without involving the US. It seems there were several plausible ways to do it. Whether that's still true, i have no idea. Interesting stuff, anyway.