You go to a country where people are starving and dying of disease. Let's assume there's only 5 bowls of rice for every 10 people. Assuming the normal course of things, 3 of those 10 people will die of Zombiaflatula (or polio, or whatever) leaving only two hungry. The flying nun swoops in with her westernized bag of medicines, and begins providing immunizations to the people that prevents Zombiaflatula and thereby reduces the death-rate, creating even greater starvation.
Of course this is a really over-simplified explanation, and as we all know Zombies don't really die, so it might work out if gas farting Zombism was actually a medical epidemic in starving Africa... but you get the point.
Does our position on Missionary aid, actually hurt people by ultimately affecting the death rates?