I have no idea how America can tax non-resident non-citizens without their nation making it more trouble than it's worth.

According to http://www.nytimes.com/2006/12/17/world/americas/17iht-expat.3928621.html one of the penalties, if you are judged to have abandoned your US citizenship for tax reasons or not paid the appropriate taxes, is permanent exile. Which certainly could be implemented by the US with minimal trouble.

http://en.wikipedia.org/wiki/Tax_exile#U.S._rules mentions something about in-US assets being subject to higher tax rates; I suppose any US assets could also be seized to pay back taxes.