I guess my statement is more accurate in recent history, post-2001. US-chartered banks are getting extremely vigilant about AML. The attitude of US bankers I've worked with is much more cooperative than Europeans, who view this AML focus as the Yankees trying to impose US law where it doesn't belong (a fair criticism).
(Yes, I know UK != Europe, but presume it's indicative)
This popped up on the BBC a couple days ago:
"Foreigners must not be able to buy UK homes with 'plundered or laundered cash' as part a global effort to defeat corruption, David Cameron has said."
http://www.bbc.com/news/uk-politics-33684098
I assume the takeaway is that it's enough of a problem that it needs to be focused on. The article cites $1tn/year being taken out of poorer countries by corruption, and $190bn worth of property in England and Wales owned by offshore companies.
I don't think this is particularly a US/EU distinction. Switzerland's history of banking privacy and neutrality, possibly.