> When it comes to antiterrorism stuff, it's a totally different story. If I go to the Middle East and provide money to an organization on the US terrorist list, then yes - I can definitely be prosecuted for it if I enter US jurisdiction. And it goes even further - I don't need to enter their jurisdiction. The US can just have me extradited if there is a treaty.

Moreover, the US government can have you seized and brought to the US without a treaty (or even in violation of a treaty), which may become a diplomatic and/or international legal issue between the US and the state where you were seized, and may subject the agents doung the seizing to personal legal difficulty in that state, but has no bearing on the validity of the criminal process brought against you once they haul you back to the US. See, e.g., U.S. v. Alvarez-Machain, 504 U.S. 655 (1992).