Hi there
I'm a 4th year student at the University of Auckland's School of Medicine. The international applicant thing is pretty new, in my 2nd year it was just starting up and there were only 2 international entrants in my class, both from the states. I don't know how many they accept now but i don't think its very many. The class sizes are around 140-150 and the emphasis is very much on New Zealand Citizens when it comes to selecting students.
I was accepted into the undergrad programme straight from high school so i don't know much about the requirements for graduates. You may also want to consider that international students pay much higher fees than NZ citizens. We pay around NZD $10000 a year but international students have fees of more like NZD $30-35000, which i guess is still relatively cheap compared to US schools when you convert to US dollars, but worth noting.
Hope this helps