What Was the Extraterritorial Scope of the Material Support Law (2339B) Between 1996 and 2004?

My post yesterday on possible civilian criminal charges against al-Nashiri included reference to my view that 2339B was not extraterritorial until a 2004 amendment.  I should have been far more specific about my claim.  Of course the statute from its origin in 1996 did include language referring to extraterritorial application...but in its original form it also specified that liability would attach only to persons acting within the United States or to persons "subject to the jurisdiction of the United States."  Here's what I wrote about this point a few years ago:

A third limitation on support liability is jurisdictional. From 1996 through 2004, § 2339B provided liability only for conduct occurring “within the United States or subject to the jurisdiction of the United States.” Depending on how broadly courts might prove willing to construe the concept of “subject to the jurisdiction of the United States,” this might preclude reliance on § 2339B for members and supporters of al Qaeda even after that group’s designation in October 1999, at least insofar as such persons were noncitizens outside U.S. territory. If so, § 2339B would not apply to the vast majority of al Qaeda members who fell into U.S. custody in Afghanistan and elsewhere in the months and years after 9/11 . Section 2339B’s jurisdictional limitation was dropped in late 2004, and thus will become less significant over time. For now, however, it remains quite relevant, including with respect to those detained at Guantanamo. IEEPA, for its part, still requires that the person or property in question be “subject to the jurisdiction of the United States.”

On this view, the "subject to the jurisdiction" language would at least encompass citizens and lawful permanent residents traveling abroad, but possibly not others such as al-Nashiri. But comments from a reader after yesterday's post have convinced me that the issue is not so clear.  The alternative reading is that the original language was meant to extend to any person abroad, whether a US person or not, so long as the offense conduct in some way connects to the traditional heads of extraterritorial jurisdiction recognized in international law (including, for example, a situation where the non-citizen's conduct endangers or harms US persons).  Well, that's not the only alternative.  It's also possible that legislators had no clearly fixed and shared understanding on this point.  It may be that the rule of lenity would require the narrower construction of the statute in light of the uncertainty.  In any event, I'd be glad to hear from any readers who have further insights on this question, whether drawn from the legislative history of AEDPA or the 2004 amendment or perhaps from practical experience grappling with this question.  And if I've somehow missed a judicial construction of this language, by all means let me know.  The point is worth pinning down if possible, and I'll post any further insights there might be.