Yup. My friend's dad had his UK account(!!!!) frozen on request of USA government because he was doing business with Cuba(trading cigars). He has never ever been to USA,and the money being transferred wasn't going through US either. It took 6 months before whichever US agency finished their investigation why a UK-citizen would be buying Cuban cigars, and they "allowed" the account to be unfrozen. Absolutely unacceptable if you ask me.

The transactions WERE going through the US, which is why the US government had jurisdiction.

Absolutely not. The US courts used the argument that in last resort a US clearing house _may_ have to survey the transaction because it was in US$. However not a single dollar went through the US.

I'm puzzled by this:

On top of the potentially huge fine, BNP Paribas could suffer a temporary ban on processing dollar transactions, a business that is essential to the operations of an international bank.

Are USA officials able to enforce these sorts of restrictions on e.g. the sidewalk moneychangers one finds in any developing nation? There are more dollars (both physical and in ledger books) overseas than in the USA. At what point does a bank in another country become vulnerable to this sort of restriction? Are officers going to show up outside the bank and yell "give us all your dollars!"?

Banks don't move dollars in crates overseas, transfers in USD are going through US banks: http://en.wikipedia.org/wiki/Correspondent_account

Hmmm, that seems to contradict the assertion that "not a single dollar went through the US". If this is the mechanism that BNP Paribas uses, they shouldn't be surprised they are subject to USA laws.