The answer, like most of the world's answers, is "it depends."

I try not to compete with local people for scarce resources. In even a mild famine, for example, the presence of aid workers can drive up the cost of already-scarce food. Travelers make it even worse. Same goes for water and other necessities. This part of the answer is relatively simple.

But the category "scarce resources" also includes things like use of transport, purchases of gasoline, police and other protection.....you name it, it's likely to be in short supply or available only at jacked-up prices following a major disaster of any sort. Again, I try not to compete with local people under such circumstances. As it happens, the government of Chile (reportedly) asked tourists to stay away for a while following the earthquake for these reasons and more.

At some point, competition for resources becomes less of a factor, but I don't claim to understand how to determine this. Obviously, as a paying tourist I can be in great demand by those who stand to profit directly (hotel owners, restaurant managers, etc.) while all the while my presence interferes with delivery of goods and services to those who really need them. If I'm not contributing directly--by doing disaster relief work, for example--maybe I should stay home or go elsewhere even when they're begging me to come.

My approach is really just a starting point, but it often dictates the terms of my travel. I don't go to the Sahel during what is known as "The Hungry Season" each year. I cleared out of Chile before arriving in the damage zone this past month. And more like that.

I'm interested in hearing more from others, since I sure don't think I've got it figured out just yet.

Mark

(from southern Brazil)

Edit to add: on another notable forum I was roundly ridiculed for suggesting that it made sense to schedule travel to avoid disaster zones. Apparently, even in its simplest form this approach has not won wide adherence among travelers.