"it's heartbreaking to just say no"

Sounds like a false dilemma; I would argue that, even if you accepted James Shikwati's analysis (which I don't), the first reaction should be to see whether it's possible to enact more effective methods of assistance, rather than immediately give up.

"What does aid to Africa have in common with healthcare spending?"

I assume "they're both politicized topics that smart people seem to disagree about" is not the answer you're looking for.