So reversing the scenario - an illegal immigrant kills me - can't be prosecuted? Because they're not under US jurisdiction?
Unless you were snuffed out on federal land, I think state law would reign in this situation, and the states can have jurisdiction over you just by being on their territory. In fact, I seem to remember a time when you could be a citizen of a state, but not of the United States, to further complicate matters.
you are arguing with people who are being academic to a fault, unable to see how they've been co-opted. that said, i appreciate the commentary from real lawyers - i LIKE academic stuff even if the real, hard embodied politics of it all is straightforward.
That question isn't really meaningful, because commission of a crime is a basis for jurisdiction.
Generally if party A commits a crime against party B jurisdiction can be claimed by (1) the country where the crime occurred, (2) the country A is a citizen of, and (3) the country B is a citizen of.