I agree, they look like square threads to me as well. I have not been part of this discussion, but have watched it from day one.
I did not speak-up, because i really do not know what it is either. But, of all the valves i have seen, and worked on, ie. globe, gate, ball, butterfly, and home, and commercial faucets, i have never seen this type of square thread used? Please correct me if i'm wrong.
edit: I stand corrected by myself, as i did make a comment on the dead center theory.