Forget teaching men to fish; repairing a man's hairlip, cleft palate or cogenital birth defect so that he can finally get a date is going to generate more soft power and long-lasting good will towards the United States than all the fish in the world.

NGOs, State Dept, and USAID are (as others have noted) often better-suited for long-term contributions, but for quick, short-term operations, the military possessess the logistical capabilities and manpower necessary to excel where others struggle. The US Navy can port at a remote Indonesian island, perform surgeries and provide medical examinations for local children, then depart entirely on their own power. An NGO seeking to do the same would have a nightmare trying to arrange transportation, secure lodging for the doctors, etc.