31 wasn't around in the 20th century (or even the 21st), at least not in a form recognizable as the Section 31 of the 22nd-24th centuries. My thinking was always that - while their missions are similar, at least in the broad sense - S31 was several steps removed what you see in
From History's Shadow and
Elusive Salvation, and that having S31 be a direct descendant of Project Sign in 1947 is a bit too simplistic. There's a huge span of time between those two points, with lots of room for adding in juicy details.