Ah, we seem to be using different definitions of productive. I was using "productive" in the sense of "effective at performing tasks," while you seem to be using it in the sense of "producing economic value--" my mistake. I think I was confused by your statement

I have no reason to think that his output is higher than anyone else who makes the same amount of $ that he does, so I don't think he is especially productive.

which seems to conflate "output" with productivity.