No, just jurisdiction over it's citizens. The USA is one of the only countries that taxes and requires its oversees citizens to file a tax return. You can go to jail for not reporting a foreign bank account - pretty insane.
http://online.wsj.com/article/SB1000087239639044459270457806...
I'd say it even trumps the regulations that are largely post-Soviet legacy in countries like Ukraine, for example.
Sure, the foriegn bank is not located in the USA ,but many of them have branches in the USA, or are in one way or another allied with US banks. All of them do business with US banks.
Thus, all of them are liable for "money laundering" which has been defined so broadly that basically anyone can be convicted of it.
So, even though they are non-US entities they are required to file forms with the IRS, and the burden is getting bigger every year, and if they don't they risk censure under OECD rules or being fined as HSBC was, etc.
It's easier to just not do business with US citizens.