Well that words shouldn't be there. But the point still stands: fighting crimes and keeping order over international waters (as the Persian Gulf is considered) is probably what a JATFCNIAH (just another typical foreign country not in active hostility) will do.
Well, there's news: NZ drew most of its constitutional arrangements and cultural influences from Britain.
Regarding the hamburgers and softball, you can draw some vast theory if you like. I'd rather say that the Marines were made welcome here and that in return they taught us a trick or two.
I dunno, I'd consider calling in air strikes in Afghanistan fairly active, at least for the blokes involved. And my best wishes to them, too.