Your answer 1 didn't occur to me, but I'll bet they want to get free AVGAS from our KC-135s!
BTW, 5th DSCS veteran!
When you ask somebody to fly halfway across the world, you have to pay for their gas, man.
I'm Australian (and ex-Royal Australian Navy) and when we put troops on the ground in Iraq in 2003, the numbers were relatively insignificant, but it was important in helping the US defer some of the criticism that it was "acting alone". This is quite often the case with US-lead military operations - other nations wind up contributing fairly small forces just to make it clear that the US has their political support - one of the most powerful gestures a country can make is to put even a small number of troops into service.
Less often, it happens the other way around - the last time Australia had to put troops into stablise East Timor, the US provided a couple of C-17s to help move them. While the help was transport was itself valuable, the real value of that was the message to the potential enemy that Australia could rely on the might of the United States to back us up if needed.
