I'm not sure there's a way that a skeptical person can ever trust that data, short of physically handling each piece of paper and manually summing up the totals. People are as much of a black box as any software.
I suppose the only benefit of people is that they are more difficult to coordinate.
The point is not using people in place of machines as trust anchors. The point is that you remove the trust anchor (or move it to the public at large, really).
In a properly run paper election, there is no individual that you have to trust. In principle, anyone can go and watch, and usually there are representatives of many/all parties in every polling place, watching every step of the process. It's not just that people are more difficult to coordinate or control in general, it's that if someone distrusts you, they can come and watch for themselves.
I suppose the only benefit of people is that they are more difficult to coordinate.