I will disagree. Jurisdiction is in the eye of the beholder. Truth is that nobody has any obligations or anyone or anything, all the courts get their authority by the guns that back them up.

Wouldn't a US citizen still have those obligations if they, for example, had committed crimes in Germany but just happened to fly back to the US before being arrested?

You misunderstood: the US government is the suspected "criminal" in this case.

Criminals abrogate themselves from that responsibility by committing the crime. Their obligations are no longer relevant until the use of force is applied to make them fulfil that obligation - i.e. they are arrested and prosecuted. It is innocent civilians (i.e. non-criminals) who are fulfilling their responsibility to NOT commit crime - criminals are beyond that point.

America is getting away with its war crimes and crimes against humanity, simply because there isn't a system by which it can have its obligations not to murder millions of people enforced by external force. Yet. That day may change, one can only hope ..

I am not any kind of lawyer, but here's my interpretation:

The usage of "legal" in this thread is highly misleading: partly erroneous and partly just a red herring. You are right about the USA national law, but that's the red herring part, because it is irrelevant in this international context with sovereign states and the ICC as parties. As far as the ICC is concerned (or rather international law and the treaty, the Rome Statute, which established the ICC) the suspected crimes were committed on party territory (Afghanistan; but also Poland, Romania and Lithuania; the latter three hosted the CIA black sites where prisoners were taken) and the USA government is not willing to prosecute themselves; so the ICC's purpose is to prosecute them.

That's why I called Llimos' position pseudo-legalist. (And also because the ICC is not a "private court" any more than the SCOTUS is a "private court".)

On the other hand, the USA is a sovereign state and its government is presumably in a position to ignore the international tribunal. This is the might part, which some are equating with a legally nonexistent right.

I don't know what exactly makes the USA different in this regard to some other relatively democratic state that finds its military and government under investigation by an international tribunal. It's surely got to do something with USA's might (power the US government is able to project across the world, e.g. sanctions) and worldwide reputation; but I think public opinion within the (democratic) country in conflict with the ICC is also hugely relevant in such cases, thus I'd say the US voters don't care about democracy or justice enough (otherwise the US politicians wouldn't dare do this, or pass the relevant laws).

For a comparison, I doubt there is currently an European internationally recognized state besides Russia and, maybe, Belarus whose governing politicians would dare defy something like the ICC; and sanctions by any state other than the USA would also carry much less weight.

Taking another look at the top-level comment, another thing that is visible in it apart from fake legalism is the "if it is legal, it is right", or, alternatively, "if it is within my might, it is right" point of view. That, too, is horrible; I guess I just didn't notice it consciously before.