Im selling this for what I bought it, but I rather like the explanation, so ...
Apparently, within the American military system, when troups would come back from battle, they would report on the number of people back. Something like '3 wounded, 1 killed, 15 alive' sort of thing. And to make this easier, they shortened the words they would say - so 1 killed would become 1k. And therefore 0 killed would be OK (and nobody killed is a very good thing, so the expression became widely used to express something positive)...