American troops left Iraq nearly a year ago.

Wrong. There are currently 15k to 16k Americans working in Iraq, under the auspices of the State Department. I guarantee they aren't all working desk jobs and God knows how many mercenaries...I mean contractors are still running around. Just because they aren't labelled "combat troops" doesn't mean they don't carry guns and kill people.

Those are not troops. Are Americans working or visiting, say, New Zealand to be considered an occupying force?

Do Americans working or visiting, say, New Zealand have legal immunity from murder prosecution? Were they imposed by an invading army?

Yes but the all-encompassing rhetoric about regional political stability is just dog whistling about oil price stability [1].

[1] Alan Greenspan