I disagree, the fact that there exist a particular scenario that does not lead to the optimal situation does not legitimate the fact that it's ok to profit from poor people in general.
I'll have to admit that that was a stupid example, but my point is still that entrepreneurial people are often profit driven, and when one takes this incentive away, they tend to direct their efforts towards more profitable things. So if we deny the possibility of profit from helping the poor, we are effectively denying them any/most advances made possible by entrepreneurial people.
But what incentive would entrepreneurial people have to help the poor if not profit? It's nice to be nice for the sake of being nice, but it's also important to eat.