The "Weaver Stance" and other similar two-handed stances were not popularized in shooting culture until Jack Weaver used a two-handed stance to convincingly win a shooting competition in the late 1950's. Weaver wasn't the first to use a two-handed stance, but his victories were the catalyst that led to Jeff Cooper's American Pistol Institute, which led to widespread adoption of two-handed techniques.

Prior to this, the popular stance for just about all pistol techniques was what is now commonly called the "Bullseye Stance" as demonstrated in your linked picture. Two-handed stances existed, but were not popular or widespread.

From a media standpoint, having a modern military or police character shoot one-handed is a common trope when trying to portray them as old-fashioned.

Most of this information can be pieced together from shooting enthusiast magazines and websites, though it's tough to find hard facts and good documentation.