You could cure a lot of cancer for $1 trillion. By turning the offer down, are you sure you're not "influencing" someone else's mortality? (That's a rhetorical question, of course. I don't have an answer.)
So, I did say "any amount of money", not any amount of lives. I do think it's morally okay to trade one life for many (definitely ambiguous in terms of amounts because I don't feel like trying to figure that one out). In fact, I don't think you could justify war without also justifying this moral decision so I don't think it's very rare even if people don't often think about it.
