The book "Krupps, the Story of an Industrial Empire", by Gert von Klass, (Transl., by James Cleugh, London 1954), states that while Krupp's fame was established by gunmaking, the turning point of their financial security was established by a large order for railway wheels. Chapter 4, "The Rings" states: "These (seemless railway) tyres were for years the main articles he produced. Accordingly, it was from this branch of his work that he took his trade mark. The world famous symbol of three rings simply represents three interlocking tyres".
In the same odd way, the town of Suhl was originaly known for shoe-making before it became a centre of gunmaking, and your barrel flat has a shoemaker's "pick and sole" inside a shield (above the 16/70), which is the town's symbol to this day.
"JP Sauer & Sohn, The Story of the Oldest Weapons factory in Germany", (Arfmann and Kallmeyer, 2004)states that the East German Sauer Model VIII from Suhl sold for 300 DM around 1952, a specialy discounted price achievable because of state subsidies, compared to 500 DM for the manufacturing costs alone for the West German product. So yes, the former may have been originally cutting some corners.
I chap I know inherited his German Grandfather's JP Sauer post-war Model VIII. I only saw it briefly and a while back, but I'm sure it had "olympic" style interlocking rings too. I'll drop him an email to see if he can add anything of interest such as the production date.
